From the brochures:
Carnival: "Shorts and t-shirts are not permitted in the dining room during dinner, but are acceptable in the seaview bestro."
Princess: "In the dining room, items such as cutoff t-shirts, halter tops and torn jeans are not permitted and shoes must be worn at all times."
RCI doesn't tell you what not to wear, only what you should wear. Jeans and shorts are not mentioned.
My point is that jeans and shorts are actually not "forbidden" on most cruiselines. As you can see from the 3 above, shorts are only mentioned once, ironically enough, by Carnival, the most casual of all the lines. Of course, I have seen different wording on the websites and actually posted on the ship.
I don't think jeans or shorts are appropriate for the dining room, myself. Think of what you would wear to a really, really nice restaurant at home and dress accordingly.
Carnival Elation March 11
Carnival Imagination Sept 07
Carniival Sensation Dec 06
RCI Sovereign of the Seas Sept 06
Carnival Miracle Sept 05
Carnival Glory Sept 04
Carnival Fantasy Jan 04