Don't forget this
from Cause and Effect
I would argue that this example would not qualify as either being "alternate" or a "comm-badge."
1) The Bozeman traveled forward from the past and to the future, so it was obviously the insignia of the time (the TOS movie era); too, if we accept that the Bozeman is indeed from relatively the same timeframe, we know then that those badges were not in fact communicators but simple rank insignia pins.
Since we're hung up on comm badges, I suggest we list all the episodes where alternate comm badges were used.
Why we're at it, can someone explain why Picard wears an alternate uniform (an open coat), somewhere around season 5? It looks dodgy. This is not a quiz question, just curiosity.
Patrick Stewart wanted an outfit that would, as captain, distinguish himself/Picard from the rest of the crew. It probably also helped that the alternate uniform tunic with that jacket looks like it's 100 times more comfortable than the actual uniform he wore otherwise.