Quick succinct question:
Is it possible to add servers that are not "DICE" servers to the favorites menu in Battlefield 3 on Playstation 3.
The option always seems to be greyed out when I've viewing a server other than a "DICE" server.
No it's not possible, sorry.
This is probably due to the fact that they are the standard Quick Game servers which most likely change, start and stop based on demand. For example if there are no Caspian Border maps currently available a server might change it's map rotation to suit.
This is all just a guess at why you can't by the way since searching the interent for solid reasons was unsuccessful :(