Audio problem: Tiger is heard barking as he runs down the stairs, but it's obvious the dog isn't barking at all. (00:06:05)
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)
Revealing mistake: When Peter is on the trampoline, instead of saying "Peter," Carol says, "Go get 'em, Chris!" and a few minutes later the same thing happens after Cindy has a turn alone, you can hear Greg say "Why don't you give it a try, Eve?" (00:18:10 - 00:19:50)
Continuity mistake: When Bobby attempts to climb the treehouse for the second time, he climbs to the very top and looks up in fright. From his POV we see he has two more wooden bars to climb, despite being at the top a split second ago.
Answer: The dangling bracelet was used for dramatic purposes - to keep the audience on edge.