I have carefully read all the rules and errata and have come up with a question regarding the use of the Power Card - Doom. Does the extra power die stay black for all levels, or does it go up to the current level of the monster group?

it is a single black die.

I can't remember if FFG officially answered this question in the FAQ or not, but common wisdom on the subject is that anything which predates RtL and gives "a black die" or "a power die" as a bonus should be read as providing "a power die upgrade " in the AC game. So "Doom!" provides a single pip through all campaign levels, however, if the monster in question has five power dice already, he can still use Doom to upgrade a black to silver or a silver to gold, for example.