Is there somewhere a list of tests to be done on a new port to consider it beta/production quality?
Nope.
It would be a good idea to have such a list. Another thing that would be good would be to have a set of scripts that exercise as much of the functionality as possible.
Just using it would not be enough because each user probably does almost always the same things and don't exert the code.
Quite true. The beta label is generally removed when
- the port has been available for a while
- no major outstanding issues are known
or
- someone asks to have the beta label removed, and no one objects
