I think (and please correct me if I'm wrong here as this is just what I've gathered) the main contradiction comes in the introduction of man itself. The Bible says that Man was created in God's image. Fairly straght forward, I don't think there's any debate that that's what the Bible says and means. However, the evolutionist (which has evolved (teehee) from Darwin's original claim so the two are not synonymous) claim is that everything had a common ancestor, and the first thing that started to resemble man actually came when the Apes'/humans' ancestor split into an ape ancestor and a human ancestor. The Human ancestor then evolved and evolved and evolved untill you had the Cro-Magnons and the Neandertols, untill the Neandertols died off and Cro-Magnons were allowed to spread the world peacefully and evolve untill we're the talking, walking, thinking (most of the time) Human that we are today.
And that's where it contradicts the Bible. The Bible says that God created man in his image. However, the Creationist belief says that Humans and apes evolved from a common ancestor, so God would look a whole lot more like a monkey than a man if this were true.