Dropping your MP3-based podcasts into the 'Audible' folder on your Kindle or SD memory card will allow you to see the podcast in Home. When opened, you can bookmark, pause, fast forward, etc., just like you do with an audiobook.
This tip (from the Amazon Tips & Tricks page, thanks runciter!) seems to be a way around the normally random play of mp3's. It sounds like by putting your mp3's in the Audible directory you can actually select what you want to listen to, can someone with a Kindle in hand confirm that that's the case?