The starting point is to discuss the dispute on the talk page. If you go to the talk page of a controversial article then often you get pages and pages of discussion. And then you will find archives of more pages and pages. Sometimes they reach mutual agreement through discussion. But often that doesn’t work and sometimes mutual agreement is impossible.

The best way of settling content disputes is the “Request for Comments” where you state the issue carefully, usually on the article talk page or a project talk page, and then ask uninvolved editors to join in and post their opinions on the dispute. It usually has a section where you can post your view as “support” or “oppose”, sometimes many different options. It would look like this (example from Wikipedia:Requests for comment)

RfC about the photo in the history section

Should the "History" section contain a photograph of the ship? (signature)

Survey

• Support' inclusion of the photograph, which helps the reader. (signature)
• Oppose , it isn't relevant enough (signature)

Threaded discussion

I have concerns about this photograph. (signature)

What kind of concerns? (signature)

Some editors will just say “support” or “oppose” and then sign their opinion. But others will explain their reasons, in a short comment, and sometimes may say “strong support” or “strong oppose”.

After the RfC is over, after a set period, or when everyone has stopped commenting, then an uninvolved editor will close it and say what the outcome was. Sometimes the participants all agree as a result of the discussion or the decision is clear enough so that the outcome is obvious.

There’s usually a discussion area too, and some things may get thrashed out in the discussion, often leading for instance to the RfC being rephrased or a new RfC started.

For an example of a recent RfC which had a simple clear outcome there is this one, about whether to use the word “Persian Gulf” or “Arabian Gulf” for this stretch of water.

Should this be called the “Persian Gulf” or the “Arabian Gulf” on wikipedia, or perhaps sometimes one and sometimes the other? The result of the RfC is that it should be called the Persian Gulf. For the reasoning, and votes, see RfC: Persian Gulf and Arabian Gulf Since everyone who responded said No to the idea to call it the Arabian Gulf the closing editor had an easy job there. For the background to the proposal see the Persian Gulf naming dispute

I’ve added an example from the Bush article mentioned in the question to show how it goes in a comment - in that case there was a lot of discussion, many alternatives suggested, final outcome was not to mention the topic at all.

TRY YOUR HAND AT VOTING IN AN RFC FOR YOURSELF!

You can find a list of all the current RfCs on wikipedia here: Wikipedia:Requests for comment/All - Wikipedia If you are interested in any of those, do join in and help with the decision making processes on wikipedia. All editors are welcome to respond to any RfC including ip users, i.e. people who are not logged in or even don’t have a user account there. You can read some of the guidelines for responding here: Suggestions for responding

RFCS WITH NO CONCLUSION

Many RfCs end up with no conclusion. Part of the problem is how to attract people to vote in RfCs. Hopefully I’ve helped in my small way by suggesting readers of this answer join in to any RfC that interests you.

You have to be careful to advertise RfCs in a neutral fashion so can’t tell all your friends to vote, or tell people which way to vote and then post a link to the RfC to vote for your views. So it was okay to suggest you pick an RfC and join in but at the other extreme, it would definitely not be okay to say “please vote for this one, I know you will support my views on the matter”.

As a result it’s sometimes a bit hard for participants in the RfCs to do much to advertise them and they often just end up with all the original participants in the discussion stating their views yet again, and then one or two others, if you are lucky, join in and add their views. And often the original editors dominate the discussion that follows which can drive away people with other ideas who might take it to new areas.

So RfCs work but only up to a point. Then editors resort to other methods. Articles there sometimes “flip” so you come back a month later and find it says something completely different from what it said on your last visit. That’s because it’s got a new editor or group of editors with new views on what it should say. It might not be a result of discussion at all - just a new editor with strong views on the topic.

On articles with few editors, often one editor will “own” the article and simply revert what any other editor does. If they can find a few friends who agree with them and support their actions then it is often impossible for anyone else to go against them. For more on this see: Wikipedia:Ownership of content

I don’t think wikipedia has really sorted this out. It’s the main reason why there are a lot of actual out and out mistakes there, especially in minor articles. A wikipedian with a strong opinion who “owns” an article may be able to ward off any number of experts and professors or whatever who try to get the article changed. They can do that easily because they will generally come along one at a time and that makes it is easy for an editor with a few friends to revert their edits and send them packing.

It does seem to work reasonably well with high profile articles with dozens of editors. For an example of the sorts of things they fight over, written up in a humorous tone, see Wikipedia:Lamest edit wars - Wikipedia

Container of gasoline? petrol? fossil fuel? benzine? gas? a mixture of refined combustible organic liquid compounds for reciprocating piston engines equipped with spark plugs

One of the example long running disputes in the Lamest edit wars. Sometimes a single sentence or a single word you read there, or the placement of a full stop is the result of pages and pages of text on the talk pages, as well as edit warring (reverting each other’s edits) with many resolutions and RfCs. See Wikipedia:Lamest edit wars/Spelling and punctuation - Wikipedia

Another example from that page is the long running dispute over the spelling of Aluminium / Aluminum. This gets so many comments that it has a talk page of its own with three archives of past discussions of the topic. The decision so far is to use Aluminium with the extra i, but they continue to debate it occasionally. See Talk:Aluminium/Spelling - Wikipedia

NO EDITOR IN CHIEF

The main problem is that admins are not able to judge on content disputes. They won’t read any of the cites as they are not topic area specialists, and are not expected to be, that’s not their role in Wikipedia. There are no “editors in chief” there.

There is a Dispute resolution process, but because there is no editor in chief to settle the dispute, this is just a way to get the editors to talk to each other, with a mediator to help settle their differences. Nobody except the editors involved in the dispute will look at the sources during this process either, at least not in detail and probably not at all. The moderators of your dispute won’t know anything about the topic that is in dispute. So this only works if both sides are in agreement that they want to do it first, and if there is a fair bit of common ground and a willingness on both sides to find a compromise solution.

When it is yes / no situation with only two possible outcomes particularly, a compromise is likely to be impossible. Also if either of the disputing parties is unwilling to compromise, and are just sure they are right, dispute resolution is impossible, and this is often the case.

WHAT HAPPENS NEXT IF NONE OF THOSE PROCESSES WORK

This is not how it is supposed to work. However, because the admins don’t judge the content like an editor, they have to judge on behaviour instead. So, if editors want to resolve it by going to a higher level, and dispute resolution didn’t work or was not possible at all, often opposing editors in an ongoing dispute eventually resort to banning the opposing editors from mentioning the topic of the dispute anywhere in wikipedia. They may also block them (this stops them contributing to wikipedia at all) for a period of time. This is a very heavy handed way to resolve a dispute of course, and not at all according to the guidelines.

They may feel justified in doing so because they find the other editor annoying and think they are wrongheaded. They may feel they are protecting wikipedia from disruptive editors who are trying to destroy it. Since the aim is to get them topic banned or blocked, they have an obvious incentive to paint the opposing editor to the admins as being more disruptive than they are. It might often be that the only thing that is really disruptive is that they have a different view from the filing editor.

You can be banned for simply writing a lot in support of your own views on the topic on talk pages, never editing the article itself. I’m an example of this. I have just finished a six month topic ban on the “Four Noble Truths” - I was not permitted to mention that phrase anywhere in wikipedia. It was all the result of a talk page discussion on a single article.

I followed all the wikipedia guidelines, everything cited. No original research. No edit warring, indeed I didn’t edit the article at all except to add a “citations needed” tag which was removed and I never tried to add it back in again. No personal attacks, all content focused, academic discussion of the topic.

In the topic ban decision by the closing admin for my case, the only complaint against me that they supported was that I wrote too much on the talk page for the article and did too many edits of my comments there.

In my case if I'd had any warning I'd have just stopped commenting on the dispute or I'd have slowed down to e.g. one or two comments a day. There was no need to get me topic banned to do that. But they didn't even try talking to me about the issue first before taking me to ANI.

You almost never get anyone filing for a block or ban of this sort if they are in agreement with an editor’s views on the content (apart from obvious cases such as vandals and spam of course). I think admins need to be more aware of this when judging cases of this sort. Basically the filing editor just about always has an axe to grind and their statements can be expected to be biased and often contain misrepresentations and outright lies. Too often the admins just take everything the filing editor says as correct, as they are adept at presenting material from past conversations as “diffs” to make their case seem convincing if you don’t look too closely. The admins don’t have the time to go through these in detail and some of the experienced editors there who file these cases rely on this to win the cases (the ones who resort to such tactics that is).

As well as that, a lot of the topic bans and blocks are the results of actions by unblockable editors. These are editors who can’t be disciplined because as soon as they are blocked or banned, another admin will come along and lift the sanction For details about how this phenomenon happens, and why admins can’t do anything to stop them under current wikipedia guidelines, see this post by a wikipedia admin, User Beeblebrox, about unblockable editors. This makes it very easy for them to block or ban other editors - they can say the most outrageous things and then if the other editor rises to the bait will take them to the admins for saying much the same things they said to them, knowing that they can’t be disciplined in turn themselves.

For more examples including the case of Clarawood123 who was chased out of wikipedia just for writing about the place where they lived by an editor who claimed it was a “Conflict of Interest”, see also Robert Walker's answer to What are the most frustrating aspects of being a Wikipedia editor?

There may be things that we can do about this. First, if you are an experienced wikipedian you might be interested in my What you can do about the Alice through the Looking Glass world of Wikipedia Editing - Right Now

And for longer term ideas, see also Ideas for wikipedia reform for the long term

See also my answer to Is Wikipedia biased?

So in short, the system works pretty well for the high profile articles with lots of editors. Not so well for articles with few editors. Many areas are excellent but others are not so.

HOW TO EDIT WIKIPEDIA WITHOUT GETTING INTO TROUBLE

If you want to work on wikipedia, and want to do major work there, e.g. fill in some big gap in their coverage (they do still have large gaps in many specialist areas) then it is best to start with a non controversial topic. And - it is good to get lots of colleagues or friends involved in editing along with you. So long as there is no dispute in progress yet, there is no problem doing that and it doesn’t count as canvasing.

And if you have an article with lots of editors then it is much less likely to be destroyed or dramatically rewritten than a long article by a single editor. For professors and experts same as for anyone else. Try to edit the article as a group of several of you rather than as a sole editor and you are much more likely to succeed.

Two or three editors is good, a half dozen is excellent. Just editors of integrity, don’t need to be that you all agree, indeed a diversity of views is great. Just try to ensure that there are enough there who are involved in the article creation / editing so your content can’t be hijacked by a lone editor with a couple of friends and with an off the ball idea about the topic, who decides to do a massive rewrite of it.

If a dispute does break out, then that’s the time to slow down. When you feel you have to reply, that’s often a sign that it’s a good time to take a break. A few comments stated clearly and calmly - and then you say nothing more for a day or two, will have much more impact than a long dialog in which you answer every point. Other editors may join in and make the points you would have made. Or if not, after a long conversation with the other editors ,to come back in and make a few points in a calm fashion again will work much better than to try a ding dong answering everything they say.

For more on this see my How to edit wikipedia without getting into trouble