Many creationists like to take some lesser-known or lesser-understood (by the general public) details, or recent discoveries, related to the theory of evolution, and spin them around and claim how they challenge the theory and are evidence against it, when in fact there's absolutely nothing problematic or controversial about them, they conform perfectly to the theory, and in some cases may even be the opposite, ie. they confirm the predictions of the theory. However, the creationists' typical target audience is too lazy or ignorant to check the facts for themselves, so they get the impression that new discoveries are indeed disputing the veracity of the theory.
One of the most commonly used ones is the theory of punctuated equilibrium. Most typically the creationists either don't understand what it's saying, or are deliberately distorting it into a straw man. Even in the few cases where the creationists' description is relatively accurate they still manage to make it sound like it disputes the evolutionary theory, when in fact it does nothing of the sort.
In short, what the punctuated equilibrium hypothesis is positing is that when the environment's selection pressure is very high (usually due to a radical change in the environment, either because a group of animals moved to another location, or because of changes in climate, or a natural disaster), it may cause species to evolve relatively rapidly (compared to their usual rate of evolution.) In other words, it may happen that changes that normally may take tens or hundreds of thousands of generations might take just a few hundreds, or such. This relatively rapid rate of evolution can cause apparent jumps in the fossil record (because, after all, only a very small portion of all living beings get ever fossilized; fossilization is a very rare event.)
There's absolutely nothing strange, outrageous or revolutionary about this hypothesis. It's completely in concordance with the theory of evolution, and it's backed up by tons of evidence. Evolutionary biologists have zero problems with this, much unlike creationists claim.
Another aspect of evolution that's sometimes used as a straw man by creationists is parallel evolution. What this means is that two completely distinct and unrelated species ("unrelated" meaning that their most recent common ancestor is extremely far removed in their evolutionary tree, possibly even millions of years) may independently evolve strikingly similar characteristics.
There's nothing strange about this either. To understand why it's not something unexpected, let's take a simple example: Two completely unrelated species of mammals may both evolve very thick fur if both live in a very cold environment. If their body shapes where somewhat similar to begin with, they may end up looking similar overall after they get thick fur, even though they do not have any kind of recent common ancestor. There's nothing strange in this, and this is completely in accordance with, and predicted by, the theory of evolution.
There are rare cases where two species independently evolve a similar-looking and quite peculiar and unique feature. This feature might be so unique and unusual that at first it might appear to be strange that they just happened to get it independently. However, like with the fur example, there usually is a reason behind it. This happens quite rarely and it may be unusual, but it's nothing strange nor does it challenge the theory of evolution in any way.
Although this example is from geology, not from biology, creationists always collate the two things. (After all, to a creationist "evolution" encompasses the vast majority of natural sciences. They can't even agree on a clear definition.) When looking at the so-called geologic column at some place where it's visible (eg. on canyon walls etc), oftentimes layers of entire eras are missing. Of course evolutionists take this to mean that the entire concept of "geologic column" is just a fraud.
To a geologist this isn't anything strange, and any competent geology textbook will explain this. The reason why some layers may be missing at some places is because of erosion. What happens is that the height of the ground is usually not static, but ground level may raise and lower over thousands and millions of years. When a large area of ground raises due to geological events, its top layers may start suffering from erosion (basically, wind and rainwater erode its top layers away.) When that area lowers again in the future, it may start once again accumulating new layers. This causes jumps in the layer structure, hence the "missing layers."
What creationists fail to mention is that the layers that are not missing are always found in the same relative order. They also fail to mention that usually if you traverse eg. the canyon further, there usually comes a point where the missing layers start appearing (and other layers may start disappearing.) This is all due to erosion during the geologic history of the place.
Of course creationists deliberately ignore and dismiss all this, because it doesn't suit their agenda.