So after watching the eloquent Matt Cutts on the Google webmaster youtube channel explain how great Google is when it comes to dealing with 301s and how it's just a simple matter of 301-ning the old URL to the new one, I carefully wrote code to do mass 301 redirects from my old web app to my new one.
Everything was going fine for a couple of weeks with Google still sending traffic from search results based on the old URLs which were 301 redirected to my new URLs.
Then last weekend traffic basically dropped to about 10-20% of what it was before. I know it's probably got nothing to do with this whole panda thing because parts of my site on the same domain which didn't get redirected are still getting the same amount of traffic (in fact a little bit more).
What Matt Cutts doesn't tell you is that if you are doing mass 301 redirects, Google logically gets confused and basically has to do a reset of sorts with your pages and, in particular, your links - many of which don't exist anymore if you have gone so far as to change them to the new URLs which. In effect, this results in a significant drop in Google SE traffic.
I'm expecting/hoping to recover from this eventually. How long it takes, who knows.