The following is a partial list of logical fallacies that is relevant to this controversy. Many are taken from or adapted from Carl Sagan's essay The Fine Art of Baloney Detection in The Demon-Haunted World (Chapter 12). There are many other sources from which you can find extensive lists of these fallacies such as introductory logic and philosophy texts.

Ad Hominem – Latin for "toward the man." The person confronting an argument will attack the person making it instead of the argument itself.
Common example: "This guy's a crooked politician, so how can we possibly believe him?"
Evolution/creationism: "How can we accept this from a person who is obviously an atheist (or) fundamentalist?" Just because your opponent happens to be anti-religion or pro-religion, this doesn't mean that their argument is false based on who they are.

Anecdotal Evidence – this is a claim based on an untestable assertion. In order to accept an empirical fact, it must be observable by anyone, and it must by repeatable.
Common example: "A friend said he saw a UFO, and he's not one to tell lies." It may be so that this person is no liar, but that doesn't mean he's infallible. We all are.
Evolution/creationism: You can find two sets of dinosaur footprints in the limestone beds of the Paluxy River, near Glen Rose Texas. The smaller set is of almost human size, and some creationists see this as evidence that people and dinosaurs co-existed. The idea that these smaller tracks are human has since been debunked (they do not even look like human feet), and many creationists have abandoned this argument as well. This is anecdotal as it is only one example (a misinterpreted one at that), whereas there are so many dinosaur tracks where there is no doubt about their animal affinities. For a much more detailed account, please see Glen J. Kuban's webpage The Paluxy Dinosaur/"Man Track" Controversy.

Appeal to Democracy – this is the belief that if the majority of the people believe something then that certain something cannot be wrong.
Common example: If a million people believe that 2+2=5 and one person says, "No! 2+2=4!", who then is correct? If a million people make the same error, it is still an error.
Evolution/creationism: "Over half the people in the United States believe the Creation version of our origin. They can’t all be wrong."