On mobile (Chrome on Android), I'm not seeing any way to view older podcasts.
On videos, there's tabs below the latest video for "Latest Videos" and "x Comments", but podcasts just show the comments and no way to see old podcasts.
Podcasts seem to be the only section of the site that won't let you view old stuff (News, Games, Videos all show old content). The only way around this is to look at the front page and dig deep to find when a podcast was posted.
I don't normally listen to podcasts on my phone (I use an iPod), so I just download them as needed through the website.