I can't recommend that method, MacInWin, since a user could EASILY press the home button, see the wiggling, and accidentally delete the podcast app FAR too easily.
...CLIP.
Don't think so, chas_m. If you press the home button just once, or too slowly double click, it just takes you back to the number one springboard, or beyond that to the search screen. If you accidentally triple click, the colors on the screen reverse, which is a neat parlor trick, but not much utility there. (It is a quick way to darken a totally white screen, though, which is useful when reading at night!). If you double click properly the springboard is greyed out and a new bar appears at the bottom with just the running program icons. You can swipe right and left to see more than the first four. If you swipe to the right past the running icons you get to the controls for Music, and on the iPhone, the orientation lock. Once you find the running program you want to end, you tap and hold until the X appears and then tap the X and it quits immediately. Because the springboard is greyed out, it's not possible to delete the program, and the icons on the springboard don't shake behind the greyout. If you tap in the springboard, the icons for running programs disappears immediately and the springboard un-greys but the icons are not shaking. That tap on the springboard area cancels the double-click to show the running apps.
If you tap and hold on the podcast icon on the springboard until all of the icons get the shakes and then tap the X, you get a warning that you are about to delete the app. The two actions are entirely separated and different, so it's unlikely that you accidentally delete the app instead of shutting it down.
Your suggestion to the OP to use the controls in the Podcast app itself is good, but if the OP forgets, a quick double press on the Home button will let him shut it down, too. He can also get to the app by tapping on the app icon on the springboard again, and it should reappear.
Bottom line, the double click is how Apple designed it to stop running apps, and it's unlikely to lead to an accidental deletion of the app. It can happen, but not EASILY.