In my opinion, Men being given the rule of Middle-earth was arguably the right choice. I say arguably because, as the question points out, Men are weak and corruptible by nature. I don't think anyone can refute that, though they could argue it perhaps. But I think that even though this holds true for Man in general... like here, the Men in Middle-earth had heart and perseverance. Men learn from mistakes made, in general, and do their best overall to make things better. Though there are a few in every crowd that are just plain old bad and nothing can be done to turn them from their path, I think on the whole the Men were the right choice because of their ability to adapt and to change to their environments both physically and even politically. Had a race like the Elves been given the rule over Middle-earth it would have been a different place surely. But could anyone say definitively better? I don't think they could. Elves are more wise, more steady, and longer lived than Men, but I also think that because of that they don't take to change very well. Their world is more constant and doesn't do much in the way of deviating from their preferred path. Because of that, I can't say that it would have been better. Just different. Certainly the events of Middle-earth would have been different if any of the other races were to rule it simply because they would have made different choices based on the climate they faced. I can imagine a place that would be a bit closer to Utopia had the Elves ruled, though it may have been a bit more rigid. Had the Dwarves been given the opportunity, I can imagine that there would be a very big economical climate what with their mining of various items like gold and precious gems (Thorin's ancestors come to mind) which would shape the world differently. In the end, however, I think Men were the best choice despite their flaws because of their malleability in terms of change, their ability to learn and grow, and their willingness to defend their world from evils like Malkor and Sauron.
To know you are ignorant is the beginning of wisdom.