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.
Dough Re Mi - S3-E16
Plot hole: Greg bought a time spot in the music studio to record a song. He writes a sudden new song for the studio at the last minute and then, next scene, the kids are singing the song in the studio along with background music playing. Where did all the instruments come from and who was playing them? Even if pre-recorded, Greg and the other kids would have just shown up at the studio at their time, and no way they would have been able to get the tracks down in advance to an unknown song like that.
Answer: The dangling bracelet was used for dramatic purposes - to keep the audience on edge.