I agree with F-Mattox on this, if you are a person that tends to get cold easily, bring a nice sweater. My wife has to wear one in the ship (the theater and dinning room sometimes) because it is normally kept pretty cool in the ship.
I don't think they would say anything if you wore "dress" Berumda shorts. Especially if you had heels and a dressy shirt. But it wouldn't hurt to bring a pair of slacks or something in case you find the dinning room is too cold.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007