Ok, here's my free idea of the day. I'd like a water-resistant plexiglass housing for my iPod. It would mount to the mirror at eye-level by that semi-permanent foam tape. It'd have a shelf with a lip that the iPod (or other MP3 player would sit on), a band or other mechanism to hold it in place, and then a plexiglass front cover that pivots at the top. A groove at the bottom would allow your earphone cable to come out.
The idea is that you can watch a TV show or movie (or listen to music) while shaving without having to precariously balance your iPod on top of an ornamental vase (vahz). It would be for times when you're not accessing the controls much, when you set it to play and leave it be. While not entirely watertight, the enclosure would be designed in such a way that it'd be really difficult for simple splashes to get inside.
If someone decides to manufacture such a case, all I ask is for 1 free case -- and 1 penny per 100 shipped to retailers.