The main ethical implications are for planetary protection, and also safety of the crew.
PLANETARY PROTECTION
If we accidentally or deliberately introduce Earth microbes to Mars before we know what the effect will be, we could be robbing ourselves and our descendants of discoveries in biology as significant as the discovery of the double helix structure of DNA, or the discovery of evolution itself. It could be that significant, what we might find if we find either some early form of life on Mars, e.g. RNA world life with no DNA or proteins, or some other form of life made extinct by DNA life on Earth - or some exobiology based on a totally different biochemistry. Also, some of the things we could find there might be very vulnerable to introduced Earth microbes.
Humans aren’t the problem but the microbes that accompany us are. It’s especially easy to see this I think for Mars because the whole planet is interconnected through global dust storms which can shield microbial spores from UV light and it has potential surface habitats such as the RSLs that Earth life may be able to colonize, with many microbes and even lichens shown able to survive Mars conditions in Mars simulation experiments.
Robert Zubrin and a few astrobiologists also have put forward a bold hypothesis that what we will find on Mars is identical to Earth life in all respects, or sufficiently identical that there is no need for planetary protection of Mars. However, this is not at all proven and indeed very much a minority view.
It is indeed possible that some life has got to Mars from Earth. Microbes hardy enough to withstand the shock of ejection from Earth after a giant impact (such as the one 66 million years ago), re-entry and impact on Mars, a century of extreme cold, vacuum and cosmic radiation - and to survive the percholorates, and to find some habitat they can survive in when they get to Mars. There are some lifeforms that can do all that but we don’t know if they have made it ot Mars. Most Earth life certainly hasn’t and wouldn’t last even a fraction of the time needed for that journey. The easiest time for this to happen is in the very early solar system over three billion years ago.
As an example of what we might find on Mars and might be vulnerable to Earth life - the shadow biosphere hypothesis suggests that there may be RNA based life on Earth that uses RNA without DNA or proteins. We haven’t found it, but something simpler must have preceded DNA based life. The reason we can’t find it on Earth is probably because DNA based life made it extinct. So what if it still exists on Mars? Even if a few microbes from Earth got to Mars they might not have been enough to make all RNA based life there extinct. After all if the RNA shadow biosphere is a possible hypothesis on present day Earth - why not on Mars?
As a result, it is not at all proven that any life has transferred from Earth to Mars, it remains a hypothesis at present.
Also Elon Musk himself says the first landing on Mars would be very dangerous, and it’s the landing itself that is the most dangerous part. After a Challenger style accident with astronaut bodies, air, water, food and belongings scattered in small pieces over the surface of Mars, and spores blown in the global dust storms roughly every two years, that would be the end of any chance of planetary protection of Mars.
SAFETY OF THE CREW
I know many people have said they are willing to go to Mars even if there is a high risk of dying, but the situation may be very different if they are on a spaceship to Mars and the air supply has failed, or the food has run out and they face death directly, personally, not as a romantic noble ideal in their imagination. Even if they all sign disclaimers saying that SpaceX is not responsible for their safety, that probably has limited legal vailidity and their relatives could probably tie them up in claims for decades. There’s also the setback effect on space travel generally. If a crew of a hundred astronauts all die in one go, in a failed mission to Mars, what would that do to spaceflight with humans generally in the future?
For Elon Musk so far it seems to be all about payload. I have safety concerns for Elon Musk's rockets for humans, following Doug Messier's critical reviews. See for instance his Are SpaceX’s 60 to 80 Hour Work Weeks Really Such a Good Idea?
I think it needs to be proven whether his rockets will be safe enough for humans, in particular with his workers doing 70-80 hour weeks and a NASA report showing unsafe practices such as standing on equipment while working on it, which they have addressed, and stopped doing (presumably) but still, they shouldn't have done that in the first place.
They also still have the silicon valley ethos of people working 60 - 80 hour weeks and tired people make mistakes - not ideal for human occupied spacecraft. Also, the way they are doing so many changes to the hardware so quickly when you need many test flights with the same hardware to be sure of safety for humans.
He hasn't yet sent a human into flight, not even a test pilot so it is a lot of confidence and extrapolation. And will the reused rockets be as safe as they were originally?
The problem is that human spaceflight needs far higher safety levels than unmanned flight. One launch lost in 50 is fine for unmanned flight. But not for humans. And it takes a fair bit of while to establish safety for human ships. A good escape system in event of an accident on the launch pad is a good start. But will their working ethos and company practices lead to an escape system that does indeed work flawlessly when it is needed? Will they be able to approach something like the reliability of the Soyuz TMA?
The problem is that unlike cars, you can’t do many tests of the rockets. Would you drive a car that has only been tested a dozen times, to make sure it starts correctly without its engine exploding and killing everyone on board? If the manufacturer fits an ejector seat to the car so that you get ejected from it safely in the event of the engine exploding, just in time to escape the effects of the explosion, how much confidence would you then have in driving that car? Some people would drive it if they are used to such risks and only drive it occasionally and it goes somewhere they can’t get to in any other way.
As a result flying into space is likely to remain high risk for a while.
He's already proved SpaceX is a leader in unmanned spaceflight, but I see it as "watch this spot" for manned flights. Not just for SpaceX, also for all the manned flight companies. I think also that they should be sold as high risk. That much Elon Musk does do. He doesn’t claim that it is going to be safe, unlike Virgin Galactica who rather play up the safety aspect of their system I think well above what is likely, selling it to celebrities as if flying into space was similar in safety to flying in a plane.
We can’t expect them to make their rockets as safe to “drive” as a car - that’s unrealistic. But will SpaceX achieve a safety level that is acceptable for human spaceflight, with the higher risks that are accepted in that field? I don’t know yet, wish him well that they do!
So anyway this is something that is within government oversight. To check to make sure any vehicles that are used by the general public (and private companies selling rides into space do fall into that category), whether private or publicly owned and developed, satisfy the relevant safety levels, whatever is appropriate for the particular vehicle and use of it. In the particular case of spaceflight it also is relevant because of the long term effects on spaceflight generally in case of a major disaster in space.
LIFE SUPPORT
Life support for a mission of a few days is comparatively easy - lots to go wrong but we have done it many times. Longer term missions up to a few months between resupply is also proven though much harder, it works on the ISS and worked on MIR and Skylab but with a fair number of glitches needing rescue by sending emergency supplies of oxygen and equipment from Earth.
It's my understanding that many experts would say that life support is the most difficult challenge of all for a deep space mission. Getting the mass there is easy but making sure what you have keeps a human alive for years on end is tough. And at that point it is not demonstrated technology. The ISS system could perhaps work but you are talking about a new spacecraft, not sending the ISS on a deep space mission, and then you have the problems of zero g - nobody has yet survived in space in zero g for long enough to get to Mars and back except for one individual who got close to the time needed but he might have had exceptional health in zero g, he could be an outlier. And he had to do 2 hours exercise each day and was trained as a doctor.
The solution may well be artificial gravity, but that has to be tested and shown to work.
I don't think cosmic radiation is such a big issue if you can manage the huge payloads that Elon Musk talks about. You can solve it by throwing more mass at it by having lots of shielding, and also by accepting that you will have a higher risk of cancer when you get back.
But health is in zero g, and use of artificial gravity are major issues.
Then the life support systems are very complex and many gases that have to be purged that can harm humans if they build up, and oxygen generators can fail, CO2 scrubbers rail etc. And food can go off, and the ISS hasn't really worked much in practice on the problems of carrying food with you that you open and use two years later. Lots of small details to be sorted out about things like that and I'id say you need lots of test flights closer to Earth to be sure it works. And they need to be multi-year in duration so it would take longer than it did for the test flights for Apollo which were only several days in duration.
I think that before we send human missions as far as Mars orbit, all of that should be addressed. A private company might not have the breadth of vision to see all the issues especially if it is doing something that has never been done before.
The obvious answer is to go to the Moon first, where it’s much easier to support crew with any problems from Earth, and you can get back in a couple of days.
I don’t think flights to Mars should be approved until we have a fair bit of experience on the Moon or closer to had first. That includes flights to Mars orbit, which if done well are find according to planetary protection, but I think they need to be proven safe first.
And this is a situation where governments can legitimately step in, if some company is enthusiastically promoting something that is seriously unsafe beyond the limits of what is acceptable even to adventurers and people who take extreme risks. I think that might be the case for these fast to Mars plans.
Also planetary protection is a larger issue than any company as it involves making a decision for the whole world, an irreversible decision about the future of Mars for all future time, whether to introduce Earth life to it or not. I don’t think such a huge decision should be left up to enthusiastic entrepreneurs who convince themselves that it is harmless and will not get in the way of science and is beneficial for the future of humanity - unless experts internationally agree with them on that assessment.
See my Case For Moon First