One problem is that he has published almost no peer-reviewed, primary research papers, the standard way to contribute to the scientific process since... well, around Newton's time. A more serious problem is that the few substantive arguments he has advanced have been criticized repeatedly, and he has been inept in his responses (I say this as someone who is genuinely interested in some of the questions he raises) -- typically he will challenge the scientific credentials or the character of his critics, while avoiding or misrepresenting many of the serious questions they raise. (For example, see his exchange with Thomas Schneider.)
Dembski can also write some remarkably stupid (telling?) things. Pharyngula and Panda's Thumb have picked up a steady stream of these. Here's one I have just read in Philosophy of Biology on the relative merits of young earth creationism and evolutionary biology:
"[...] young earth creationism is at worst off by a few orders of magnitude in misestimating the age of the earth. On the other hand, Darwinism, in ascribing powers of intelligence to blind material forces, is off by infinite orders of magnitude."This is particularly interesting coming from a mathematician!
Perhaps this was the aspect of Dembski's output that Koons had in mind when he drew the parallel with Newton -- he was thinking of Newton the alchemist or Biblical interpreter, not Newton the physicist or mathematician.