Personally, I like the sig/wallpaper idea.

In the theme of fanart, we could also have a contest to create new banners for the site (the ones we have are getting stale), a new logo, etc.

As for the idea of trivia, I like it. However, let's face it, it's impossible to give everyone equal footing. I know for a fact that the number and types of animes seen by people here are extremley varied.