What I think is the main problem some people have with Objectivism
Its followers preach a lot about "freedom" and "individualism", but they don't really seem to have much sympathy for people who have little and must enter into unpleasant deals out of necessity. Capitalism isn't really a system of self-reliance and independence. Under that system, most people have to buy stuff from other people and work for other people out of necessity. Objectivists often oversimplify the situation by implying either these transactions are almost recreational in nature or that if those people tried harder or were more talented they somehow would have never needed other people at all.
I think Objectivists tend to be obsessed with precise, pinpoint logic. Many Objectivist articles read like mathematical proofs where some of their philosophic beliefs and axioms are stated with some facts about the situation and then the supposedly perfect solution is derived. The problem is that the real world is more complex than that and it seems to me that they simply disregard more complex problems so they can be logically consistent and believe they have got everything figured out.
I definitely believe that government intervention has screwed things up, but I think empowering private property owners too much would really result in the same thing as government controlling everything, just with different terminology. I think there has to be a balance between public and private power to maintain the most freedom. I think hardcore capitalists and socialists are people who just pick an extreme for the sake of simplicity.