One of the favorite strategies is to find a handful of examples where random evolutionists were mistaken about a particular fossil or sequence, and wave those instances around as if they "disprove" evolution. The creationist would present a false dichotomy, that science is either right on everything and every detail of that thing at any given time, or else completely false and untrustworthy. Well, that entirely disregards what science is and what it does! Science is a self correcting mechanism for knowing the world with the best possible certainty based on the information we have at the moment. Mistakes do and will happen -- and scientists amend their work to account for new information (something religion could really learn from). Science is a work in progress, always; scientists are open to correction, and change their ideas as new facts emerge (again, something religion would do well to imitate). So when a scientist discovers that he's made a mistake, and amends his work to reflect that, that is not an instance of science not working; it's an example of science working exactly as it's designed to work, of flawed hypothesis's, when put to the test and found wanting, being discarded. In the creationist worldview, though, science working is evidence that science is wrong: if it had been right, no one ever would have got anything wrong. (In which case, we might as well chuck out every bit of science we have, from astronomy to medicine, because more than a few someone's have got more than a few something's wrong along the way in every field of study we have; you'd be hard pressed to find the creationist who would give up life saving medical treatment, though, because doctors used to be wrong about something...) It's an intellectually dishonest approach reserved almost exclusively to the science of life's beginnings.
Furthermore, this discussion always tends to ignore the fact that these errors are never make-or-break points; individuals might get minor details wrong, but the overall theory stands. It's something akin to arguing that one person thinks that Jennifer Lawrence wore a black gown to such-and-such awards show, but it was really white; therefore Jennifer Lawrence can't possibly exist. Jennifer Lawrence's gown color might be a tiny clue toward understanding the overall picture of her mood, tastes and fashion preferences as relating to that award show on that particular night, etc., and wearing a different color will slightly alter matters, but the detail has no impact on the question of whether or not she attended the award show, wore a gown of some color, etc. -- and it certainly does not alter the fact that she exists!
That is simply a bad argument. The strawmen are my favorite, though. Creationists have a habit, whether of ignorance or willful misinterpretation I do not know (I think it varies from person to person), of completely distorting the theory of evolution, and then attacking the strawmen they've spawned. These tend to be the only view of evolution that they can successfully rail against: one that they, and not reputable scientists, construct and/or promote. Scalae naturae is one such notion that is often conflated with evolutionary theory by creationists (visually depicted/addressed below).
This is the source of the non sequitur "But there are still apes around! How can there be apes if we evolved from apes millions of years ago?!" This argument works on the faulty premise that the apes in question are our direct ancestors when evolution does not claim this; evolutionary theory suggests that we all share a common ancestor, but not that the gorilla or chimpanzee is our ancestor, much less that they are part of a chain of ancestors leading to us. The creationist claim is something like observing that there exists a brother and a great-great-great grandfather in your family tree, and dismissing the entire business of one's lineage because, "look, I have a living male relative, therefore I couldn't possibly have a dead male ancestor!" It is nonsense, utter nonsense. Distinct relatives should not be be conflated, combined, or confused. It is a complete misrepresentation of evolution to do so, but, of course, the strawman that the creationist cites is much easier to attack than the actual theory...
Misrepresentation is perhaps the strongest tool in the creationists box of tricks, because appeals to ego and fearmongering can only go so far, especially with a rational mind. Naturally, there are plenty of misrepresentations to be found. The Boeing 747 fallacy is one such. It relies on evolutionary changes happening in giant leaps, and argues that it is more likely that a tornado sweeping through a junkyard could assemble a Boeing 747 than [insert complex item] might have just happened by chance. I've personally heard many variants of them, from those that focus on proteins to human beings. This is a misrepresentation because biologists do not allege that mankind simply happened, that all the right pieces fell into place spontaneously, and viola! Adam is born! Change is a gradual process that takes many, many years; a random collection of bacteria, proteins, or anything else, didn't magically fall out of the sky into the shape of man (or monkeys, or plant life, etc.). That's not the position of science. The only people out there making this claim are creationists -- in their attempt to disprove evolutionary theory, by completely misrepresenting it's claims. (I should note that Richard Dawkins' chapter on this topic in The God Delusion does a masterful job of dismantling this argument; indeed, he turns it rather on its head, making a convincing case that the god notion is the ultimate Boeing 747. I highly recommend perusing it).
Another popular misrepresentation relates to the term "theory". In common usage, we use theory to mean "idea" or "speculation"; something that is true is fact, something that we're guessing about is a theory. In scientific terms, this most closely resembles a hypothesis; by contrast,
a theory is an explanation or model based on observation, experimentation, and reasoning, especially one that has been tested and confirmed as a general principle helping to explain and predict natural phenomena.Richard Dawkins had this to say on the matter:
A theory, then, in science, is not just a random guess, or even an educated guess. It's also worth pointing out that the practical application of theories plays a tremendous role in our day to day life (we avoid germs if possible, we don't jump out of tall buildings, etc.). "Just a theory" is a misrepresentation of what it means for an idea to be a theory in the scientific world.
A related falsity that the creationist will often put forth is that theories like gravity are observable -- we can drop an apple and observe the outcome -- but the theory of evolution is not.
This is to conflate "being there in the moment to watch as it happens" (this has happened, but, obviously not with our own species) with "observable". Human beings have witnessed new species arising, but the evolutionary process leaves ample additional observable evidence. It is nonsense to say that evolution hasn't been observed. It has been and is being observed. In the same way that we can observe that we had great-grandparents (even if they were long dead before we were born) through the evidence that is left behind, we can trace the origins of species. There is a difference between scientific observation and being a witness, in real time, to the event. This argument is merely an attempt to gin up incredulity: "well, gee, how do you know if something happened a million years ago? Who could observe that? I mean, were you there?"
Which brings us to yet another horrible argument employed by creationists: "Well, how do you know evolution happened? Were you there?!" Ken Ham's piece (linked above) arguing exactly that includes these illustrations.
The absurdity is perhaps best highlighted in the following (from Ham's piece; all emphasis original):
Carl Sagan's Big Bang theory is WRONG! How do we know that for sure? Because God was there—Carl Sagan wasn't! God knows everything—Carl Sagan doesn't! This world did NOT have a fiery start from a big bang, but it surely will have a fiery end with a big bang, for "the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up" (II Peter 3:10).An invisible, unobservable being bringing everything into existence with happy thoughts and magic? No problem. Observable data that indicates something contrary to the claims of my ancient, oft-revised, scientifically inaccurate tome? If I didn't see it, it didn't happen. And I didn't see it...
While the trope of creationist arguments do not actually address evolutionary theory, I would hazard a guess that for many creationists that's not really the point. They don't take on actual scientific claims, but rather tackle figments of their own imaginations in order to convince the listener that evolutionary theory is an absurdity. It seems that the point is to bolster religion's claims by making them all science-y, and little else. The irony, of course, is that creationists are preying on the science illiteracy of the listeners, on their own ignorance of the very thing they're criticizing, to convince them that scientists are foolish and ignorant. It's the blind leading the blind -- to think that everyone who can see is in fact blind, and that eyesight is itself a myth.
Creationism strokes the egos of its believers: they are not mere monkeys, but creatures of divine making, molded in the image of God! Creationism strikes fear into the heart of believers: the world will surely be destroyed by the godless heathen if we accept that we are mere animals! Creationism convinces believers that they are embracing the only logical position: (the creationist strawman position of) evolutionary theory is clearly illogical and must be rejected! Building on all of this, creationism finally convinces believers that they're special smarties for rejecting the patent absurdities of science (as they themselves have presented it): that Jesus has rewarded their devotion with wisdom, while the rest of the world goes around believing nonsense and looking like fools! This is a very strong aspect of creationism, and one borne out by even a cursory examination of creationist materials: that people who accept science are idiots, to be mocked and derided by those in the know. (I don't claim that evolutionists refrain from mocking creationists; many surely do not. However, creationism is generally mocked on the strength [or, more properly, lack thereof] of its arguments. It is standard practice for creationists to completely misrepresent evolutionary positions, but extremely rare for evolutionists to do so to creationists: a creationist has little choice, if he is to prevail against evolution, but to invent a myth to take down, whereas the evolutionist need only focus on the absurdities claimed by creationists. No myth making is necessary, as creationists have already done that part.)
This is both the strength and weakness of creationism: as long as people are ignorant of actual science, they will be susceptible to the misinformation, fearmongering and egotism of creationism. But when knowledge replaces that ignorance, people will have to either do as the Catholic church has done, and accept evolutionary theory as God's creation mechanism, or otherwise reconcile their beliefs with reality. I suspect that this will come at the detriment of belief in most cases...which might be the great irony of all of this: that creationist insistence on such a radical course of anti-science nonsense might actually backfire when people realize just how duped they've been. That would be interesting, wouldn't it?