Whoops, figured it out.

When I first installed the new LimeWire, it wsa crashing on startup. I then tried running it as root, and it worked fine. I then fixed the original problem, but by this time my 'Incomplete' folder was owned by root. Hence, any download that was attempted, failed due to write permissions. The only ones that didn't fail right away, were the ones truely stuck in a "waiting" queue...