Plot hole: At the end of the episode, the younger kids are singing the song "Girl" that Davy Jones did a little earlier in the show. The problem is that the song was just recorded and hasn't been released yet, they couldn't possibly know the song. Davy gives Marcia an LP, but it is on the same day the song was recorded, it couldn't be on there either.
Continuity mistake: When Marcia is sitting on the couch talking with Davy, the small beige pillow behind her is either up on the back of the couch or much further down depending on the shot. (00:23:20)
Answer: There were several episodes throughout the run of the show where Marcia was infatuated with a guy she went to school with. This bracelet could have been a gift from her then-boyfriend; as such, she would not want to take it off, as a sign of loyalty. A stupid thing to do, of course, but it's not a mistake for a character simply to be dumb.
Matty Blast