In their article, Top 10 problems with biological and chemical evolution, the Discovery Institute outlines their best critiques of evolution (i.e. biological evolution) and abiogenesis (i.e. chemical evolution). As an initial response, I thought to start with Problem 3: Random Mutations Cannot Generate the Genetic Information Required for Irreducibly Complex Structures.

It starts with this uncontroversial paragraph:

According to evolutionary biologists, once life got started, Darwinian evolution took over and eventually produced the grand diversity we observe today. Under the standard view, a process of random mutation and natural selection built life's vast complexity one small mutational step at a time. All of life's complex features, of course, are thought to be encoded in the DNA of living organisms. Building new features thus requires generating new information in the genetic code of DNA. Can the necessary information be generated in the undirected, step-by-step manner required by Darwin's theory?

They then comment on some possible issues:

However, when multiple mutations must be present simultaneously to gain a functional advantage, Darwinian evolution gets stuck. As Behe explains, "If more than one [mutation] is needed, the probability of getting all the right ones grows exponentially worse."

And continuing

Behe, a professor of biochemistry at Lehigh University, coined the term "irreducible complexity" to describe systems which require many parts -- and thus many mutations -- to be present -- all at once -- before providing any survival advantage to the organism. According to Behe, such systems cannot evolve in the step-by-step fashion required by Darwinian evolution. (Wikipedia link added)

Darwin himself raised the issue, "If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down. But I can find out no such case." So the challenge being raised is a legitimate one - but one that requires the demonstration that such an irreducibly complex system actually exists. As far as I've ever read, every case has failed. For example, the bacteria flagellum mechanism, it is claimed, is so complex that it can't function without any of it's pieces. It fails as a motor if any of the pieces are missing, so the argument goes. However, what is commonly overlooked is that the theory of evolution merely states that the pieces have to have some function possibly (likely?) a different function for selection to work. Despite this fact, you don't see it mentioned in the discussion on flagellum in the original article, nor have I ever seen it mentioned in any critique on evolution. That omission I think is fairly telling.

I think the problem as phrased is also misleading -- mutations aren't the driver of the "Genetic Information Required for Irreducibly Complex Structures". The selection process is the driver. The mutations are random, but the information comes from the environment. Imagine taking a million lions and dropping them randomly over the earth. Three quarters of them will drown in the oceans, another large fraction will die of cold or of heat. Only a small fraction will survive. The process that leads to their survival or not is completely non-random even while the locations of each lion is completely random.

There is a lot to respond to in this article, even this one section, but this is a start. I'll keep chipping away at it because each piece of it leads to a lot of external reading.