Yes you have to be dressed.
Seriously, the only restaurant with a written dress code is Victoria & Albert. Some others have said no swim suits, but other than V&A I've yet to see any other restrictions.
There are some people have complained about seeing others in park clothes, i.e. shorts and such at other "nice" restaurants, but there is no policy that says this is wrong, just certain people feel it's inappropriate given the status of the restaurant as a Signature Dining. These same people feel that Disney should have a policy....or that the CMs should enforce a dress code that doesn't exist. Personally, I figure if Disney can have, and enforce, a policy about appropriate clothing at one restaurant, V&A, they can do it at the others if so inclined. Since they don't, they disagree with those people who want to see a dress code in place.
So....wear clothes, no swimsuits, and you'll be fine. Enjoy your meal!