All of these ideas just popped into my head after reading the post once-over. Didn't really think any of them through, so feel free to bash them.
If at all possible, base it off of something that can run on multiple OSes. I'm not a desktop application programmer, but I would hope that isn't too much of a challenge for you. I can't speak for everyone, but I'm sure there are a lot of people that run their favorite flavor of Linux on a regular basis.
Definitely a photo-gallery section, where users can look through all the photos, or search for a certain team.
This is obvious, but make sure the UI is user-friendly. I can think of at least one team that would use this to show potential members/sponsors some of the matches/photos/media, maybe even interactive.
Maybe allow users to upload photos of their team? I guess you'd run into permissions issues, though, since I can see that easily getting out-of-hand.
But maybe you can allow certain users to upload photos and videos, that way, those who do a lot of uploading, can do so straight from the client. Delegate flags those who you trust.
Sig-generator from the app. Would be a nice miscellaneous feature.
Easy application updates. Automatic would be preferred.
That's all for now.