Per Anita at allearsnet.com:
There is only one restaurant on Disney property with a true dress code, and that is Victoria and Albert's in the Grand Floridian. All other restaurants have no official requirements (other than shirt and shoes, of course!), although the "Signature" restaurants like the California Grill at the Contemporary and Citricos at the Grand Floridian do ask that guests wear "smart casual" (no shorts or tank tops). Even so, they don't really enforce that request. Like The Pirates of the Caribbean's Captain Barbosa says, "It's more like a set of guidelines." Use common sense, and you'll be fine.