I looked in my iTunes folder (typically /username/Music/iTunes), and I found the folder /username/Music/iTunes/iTunes Music/Downloads/Podcasts. This had lots of folders with the extension .tmp. I deleted the folder with the same name as the podcast I had trouble downloading, and now I can download again.
[kirkmc adds: Even though iTunes 7.02 is already out, this hint may still be useful. Lots of people seem to be having difficulties with podcasts since iTunes 7 was released, and I've seen a handful of temporary files floating around from time to time in my iTunes folder, or in my iTunes Music folder.]

