Deliberate mistake: While Bobby's parakeet is flying around downstairs, before the bird settles down on the TV set there are two closeups of Bobby which are flipped shots, note the furniture and Bobby's PJs. (00:07:00)
Deliberate mistake: When Bobby's at the treehouse the second time for his initiation into the club, there's a boy already up in the treehouse, and after Peter takes the birdcage from Bobby's hand, the next closeup of the boy in the treehouse is a flipped shot, note the wood boards. (00:08:25)
Deliberate mistake: During Peter's party, when the girls start to gather around Peter to try and convince him that he's not dull, there's a closeup of Peter that's a flipped shot. Additionally, when everyone runs out for the fire drill, Peter's striped tie is tied very differently - it goes from grey/gold at the top to burgundy at the top.
Answer: The dangling bracelet was used for dramatic purposes - to keep the audience on edge.