Disney's paper referenced one really nifty idea, some ideas I couldn't evaluate, and a titanically bogus idea. The nifty idea was Harwitt 1981; the idea of using different sets of data to estimate the total number of important discoveries left to be made. That's a clever and really cool trick. Back of the envelope stuff, to be sure, but still very clever.
The bogus idea -- this is the big one. The idea that observational sciences aren't, because you can't apply statistical methods to a single universe with a single history, is utterly and totally wrong. I read the paper twice, to make sure that he wasn't really saying what he seemed to be, but no, that seems to be the core claim. It will undoubtedly come as a great shock to geologists, evolutionary biologists, economists, and astronomers that what they are doing is not science, and that statistical methods don't apply to their fields of endeavor. If I reach out my hand, I can touch a dozen books that supply ample refutation of that claim. That's a pragmatic refutation. There are also reasons from algorithmic information theory to doubt his characterization of science, but I'll leave those for another day.
That's an idea stupid enough that it makes me dubious about everything else he writes. And I *agree* with his core pragmatic claims, namely that 1) Big Science is quite likely a waste of money, 2) cosmologists trying to appear philosophical and religious just look stupid, and 3) anyone who thinks we're close to solving it all is smoking crack. His paper does not add any reasons for me to believe these arguments at all.
Cerkovic's paper basically spent its time shooting the holes in Disney's facts. While this is fun, the argument seemed to be "if Disney can't get facts X, Y, and Z right, why should we believe claims 1, 2, and 3?" This is good rhetoric, but bad logic. But hell, given how easy Disney made it for Cerkovic, can you blame him? I sure can't.