Yeah, I think that's rotten spots, but I'm not 100% positive. Diagnosing plant problems is something I'm not very experienced at. I highly recommend posting the pictures in the plant problem area. Maybe people who have seen it before can tell you for certain, but I would keep cutting off the black spots and leave as much else as possible. If it is mold, you should try to correct the problem instead of treating the symptoms. Get a dehumidifier or water less often, for example.