I have just bought a new copper trombone mouthpiece and it left a black residue on my lips after using for the first time. Does anyone know what this could be?
Plain copper (i.e. without any surface plating) is an uncommon material for a brass instrument mouthpiece. Maybe it's a very expensive boutique mouthpiece. Or (if it's new to you rather than new from a shop) maybe it used to be plated and someone has polished it too vigorously?
The black will be the copper reacting with skin around your lips. Probably not hazardous, but not a good look.
You could investigate getting it silver (or gold!) plated, or (much cheaper) paint some clear nail varnish around the rim to stop the bare metal touching skin.