Well, there are 2 major contentions of Darwinism that I think most of the critics (both creationists and ID proponents) would agree are the weak points:
1) That random mutations (or other random mechanics) can lead to the creation of new and useful genetic information, rather than simply jumbling around or destroying existing information.
2) That there is no limit to the malleability of an organism’s genome, in the sense that, you could change a single-celled organism into a human being, if you simply have enough mutations and enough time.
Creationist generally have more objections than ID proponents, and they aren’t limited to just Darwinism and biology, but those two points are the basic ones objected to by both camps.
For sake of discussion, let's assume the figure 100 "random" mutations per individual is correct -- it's not, but I don't have a better number handy.
Then, given the size of our genome -- 3 billion base-pairs -- and the percentage of non-coding (aka "junk DNA") of 98%, we can suppose that 98 of 100 mutations are harmless.
On average then, two mutations affect coding DNA, and those must almost inevitably be somewhat harmful.
This helps explain why in nature most offspring die before reaching adulthood.
But not always, so let's suppose that one in a thousand of such mutations actually improves its individual's chances of survival, and thus get passed on to future generations.
So a population of, say, 1,000,000 producing say, 100,000 offspring per year then might see 100 or so helpful mutations per year.
Over the course of, say, a million years, that's 100 million DNA changes, enough to make this breeding population a distinct species from its sister populations living elsewhere.
That is Darwin's theory today.
Boogeyman: "2) That there is no limit to the malleability of an organism’s genome, in the sense that, you could change a single-celled organism into a human being, if you simply have enough mutations and enough time."
But 4.5 billion years, no single-celled organism ever changed into a human, ever.
However, starting around 500 million years ago we see the first multicelled organisms, including primitive fish, and there's no reason to suppose those came from anything other than the single-celled critters which inhabited Earth for the better part of the preceding four billion years.
In short: it took life four billion years to evolve a fish, after which evolution seemed to procede much more quickly.
As for how "malleable" is life... well no bird or mammal ever became a fish, even though many birds and mammals do live in the water, like fish.
Yet they are still distinctly birds and mammals, and that surely illustrates the limitations on genetic "malleability".
Yes, evidence does show fish adapting to dry land, etc., but the time-scales were immense, and we don't see, for example, gills re-emerging when their descendants returned to sea.
Point is: there are definite limits to what DNA can produce naturally, especially in shorter time-scales.