Inconsistent application of reason or Selective observation - to accept certain pieces of information, but ignore others because they deny what you wish to be true.
Common example: "The phone always rings in the shower" This is a perception based on the annoyance of a phone ringing and our inability to make it stop (short of dripping water all the way to the phone.) But you tend to disregard all the times the phone didn’t ring while you were indisposed. You skew your own statistics.
Evolution/creationism: Many creationists accept microevolution as there is very strong evidence for this. They will however deny that over enough time the differences will be greater. You cannot have it both ways.

Non Sequitur – Latin for "it does not follow." You justify your argument based on a fact that has little or no bearing to your argument.
Common example: The Canadian Olympic hockey team is bound to win gold at Nagano. Hey, we’re Canadian. (Please don’t spam me. I was just as upset—but it’s a good example.)
Evolution/creationism: The Second Law of Thermodynamics is often used as an argument against evolution. This law states that "it is possible to completely convert work into heat, but not vice versa". As well, "there are no perfect engines". Creationists state that since it is impossible for something ordered (i.e. a lifeform) to be created from disorder, God must have thwarted the Second Law. This is a result of a poor understanding of basic physics and complexity theory. There is a propensity for the universe to move towards disorder (entropy), but there is usually some kind of order in chaotic systems. Besides, the Second Law of Thermodynamics is talking about a very specific model of the conversion of work into heat. Also see "Slippery Slope."

Semantic Obfuscation or Poisoning the Well – to introduce confusion or bad connotations by using, or not using, certain words.
Common example: using big words to confuse the issue. Like semantic obfuscation, for example. Call someone an agent of the Devil, or even worse, a lawyer.
Evolution/creationism Example 1: Here we go again with "missing links." Creationists mention that these exist, therefore paleontologists cannot say that this creature gave rise to that creature. Missing links are found all the time that show beautiful transitions—but once they are found, they are no longer "missing." So all the missing links that still exist are missing (until we find them). At right is one of the most famous of the so-called missing links: the Archaeopteryx.
Evolution/creationism Example 2: If you encounter an idea or claim that makes you uncomfortable, call it "controversial." That was you erode its credibility. Paleontologists do not consider evolution as a controversial idea as there is so much backing it up. A creationist would do otherwise. Many parents might overreact if they are informed that their children are being taught "controversial" subjects in school.