How do you view more than 20 podcasts in the iTunes app on the iPhone? When viewing a podcasts on the iPod app on the iPhone, there's an option below to "Get more episodes". When you click on that, iTunes app is launched, and you're shown the latest 20 episodes.

Is there a way to view more than the last 20 episodes? I want to download even older ones.
In the iPhone app, at the bottom of the list of episodes you will always find the link you can tap to "Get More Episodes". That is a hardwired link to that podcast's page on iTunes. This link will be shown regardless of whether or not there are more episodes actually available. 

The podcast pages in the iTunes app and in iTunes on the desktop are the same and contain the same episode list. The episode lists themeselves are not controlled or determined by Apple or iTunes, but by the makers of each podcast. Podcast makers use different feed systems (like adlib or feeedburner) and they have different bandwith limitations depending on their own usage terms. 

Podcasts like This American Life, for example, in order to minimize bandwith costs, will only keep the latest episode on their episode list. So when you tap on "Get More Episodes" you will only get a list of one. Podcasts like This Week In Tech, for example, have bandwith sponsors that allow them to host most of their back catalogue. So when you tap on "Get More Epidodes", you will get a list of fifty or more. It basically all depends on how each podcast maker handles their feed and bandwith costs. 

Hope this helps.