How can I remove errant podcast entries in iTunes?
In iTunes, edit the bad podcast (Right click on it and select 'Get Info'). It will give an error and say it can't find the file and ask if you want to locate it. Say Yes and point the podcast to one in your recycle bin that is already deleted. Actually, any mp3 file will work. You could also make a copy of an existing one to use. Then you will be able to delete the podcast and send the file to the recycle bin. You can then use the same file for the next errant podcast. 

If you are deleting the podcasts from a (smart) playlist, then use Shift+Delete (on Windows) or Option+Delete (on OS X) to remove them from both the playlist and the library.