I think that's a great question, and one I've struggled with myself (although I admit I'm not as well-read on section 508 as I'd like to be). I think it needs to be tackled in two parts.
First, in the short term, addressing accessibility in general in the Web 2.0 world, for lack of a better term, is going to continue to be a difficult endeavor. I think you need to take care to do all the sorts of things you always do, i.e., simple things like ensuring you have good alt attributes on images, ensuring that your application, even with dynamic changes, works properly with keyboard only, etc. I can tell you I'm just finishing up a huge project at work where one of the primary concerns was being fully functional with keyboard only. It wasn't for accessibility reasons, the concern there was speed of data entry, but the concerns wind up being rather similar, and so do the solutions. We put in a lot of effort ensuring that tab ordering worked even when new elements appeared on the screen for instance via AJAX functions.
Watching for color combinations is an important thing as well. I talk about this in one section of the book... frequently, when you talk about accessibility in web design, the first thing that comes to mind is the blind, but ironically those with color blindess tend to be overlooked a bit, and my understanding is that's actually a more common condition. Making sure you don't make any mistakes in that area helps.
Another tactic that lots of AJAX applications use is to put notifications at the top of the page. The reason for this is that most screen readers read in a linear fashion, so if you put those notifications at the top, a request to re-read the page will get that information out quick. Things like this can be done short-term to help matters.
All of these are really just stopgap partial solutions though, none of them address the core problems. Long-term, I think we need better technology, and I'm not sure how much of that can come from web developers. However, one thing we should all be doing is simply learning more about the various ways those with disabilities use the web. I dare say most of us web developers don't know as much about it as we should, yours truly included. Learning about the barriers will almost certainly lead to some creative solutions as time goes on.
So, there's no magic bullet with which I'm familiar, that's the bad news. The good news is I think the problem is coming into focus and a lot of attention is being brought to it, so I have no doubt we'll start seeing some good answers in short order.