The most basic contradiction of Objectivism is that according to her:
A) Nothing has objective value, only subjective values that can only be assigned by individuals, with an eye to what is in each individual's own best interests. B) It's wrong to kill or harm others for your own benefit.
The latter is an objective rule, one that doesn't necessarily hold true. Rand and her followers have never come up with a good answer to the "perfect crime" scenario, or come up with a consistent standard on exactly what a human life is worth (though if you've read Dr. Peikoff's discussions related to the Iraq War, the modern answer would seem to "very little").