I assume you're using iTunes to download the podcast...
Sometimes iTunes will wig out, depending on whether or not the server the podcast is being served from is likewise wigging out. So sometimes you get a download that says it's complete when it really isn't.
The first solution to this is to delete the offending podcasts from your subscription list. Then, UN-subscribe from the podcast, then immediately RE-subscribe to it, and redownload the podcasts. This generally works to flush out any bad downloads that iTunes may barf on.