When I am on the menu screen and I have a disc in, it can tell what game it is, but when I go to actually play the game, it tells me it can't read it. Out of the few games I own, the only one that works is Star Wars: The Force Unleashed. Brawl, Call of Duty, Twilight Princess, and others don't work. The discs are almost perfectly clean. Could it be a problem with the lens?
It could be the lens. You might have to send it in.
If your Wii stands upright, try to put it on it's side with the bottom of the disc facing toward the floor. That might help.
I've sent it in once already because of a very similar problem, but the last time it wouldn't read the discs at all; it wouldn't even tell me what game was in the drive on the menu. But yeah, I'll go try what you suggested and see if it works.
Head to your local GameStop/whatever game store you prefer and see if you can pick up a Wii laser cleaner before deciding if you should send it in. It's possible the lens could just be dirty.
Alternatively, if you have one of those CD/DVD lens cleaners with the little brushes on the disc, just pop one of those into the Wii -- though it won't just read the disc, the laser will still scan over the disc and the brushes will make contact with the laser in the process, getting rid of any dirt present before telling you it can't read the disc.
Repositioning it didn't seem to work. I was wondering if maybe the lens was dirty. I'll go get a laser cleaner and see what that does.
It could also be your Wii's model. I know that Wiis originally had trouble reading dual-layered discs, and my Wii crapped out on me a couple years ago, but I sent it in, and it was as good as new.
But then again, Brawl uses a dual-layer disc... You may still need to send it in, though.