Could be the result of a failed sync operation with iTunes. There have been a few users that have reported similar situations in regards to podcasts. The only way I have seen this issue corrected is to disable the syncing of podcasts to the device and then re-enabling it. You can do this from under the iPod's Podcasts configuration pane in iTunes.
And if worse comes to worse, you can always restore the iPod Classic to factory settings via iTunes and start from scratch, although that may seem like overkill.