Well, I don't know the Washington State regulations regarding driving with one reliable eye, but I do know you can do so up here. I know one lady (who also happens to be a teacher) who has one eye and the other is always covered up with a patch. She always has some kind of fun sticker on the patch as not to look so "scary" to the kids she teaches.
And she drives just fine. As for the one arm, I'm sure he'd need a specially made vehicle where all the controls were on one side, if not all embedded into the steering wheel. I don't know of anyone personally who owns such a vehicle, but I've seen them.
On a side note, Wilt's stub isn't totally useless. He could hold his notes with it in "Hiccy Burp", and even wiped the sweat off his face without dropping the piece of paper. He could also play the keyboard with it in "Schlock Star". I'm sure he's done other things with his stub that I'm not remembering right now. So he might still be able to flick simple switches and bars with his stub while driving. Although he still may need them specially made so he can reach them without leaning forward too much.