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.
CarnivalSensation February 2015
Carnival Dream November 2015
Carnival Fascination April 2014
Carnival Elation March 2011
Carnival Imagination Sept 2007
Carnival Sensation Dec 2006
RCI Sovereign of the Seas Sept 2006
Carnival Miracle Sept 2005
Carnival Glory Sept 2004
Carnival Fantasy Jan 2004