Fin rot often comes after ammonia burns, so even a black fish could show red areas. I hear you on the crown tails -- that's one of the reasons I did not want one. I think once you get to know your fish well, you will know what it looks like, and notice changes. Hopefully some of the dark crowntail owners will chime in on this one.
Basically fin rot, ammonia burns, tail biting, fin shredding, etc., are all treated the same way with conservative treatments: warmth, clean water, maybe some aq salt, maybe some stress coat.