Revealing mistake: The wall behind Mr. Brady's desk at work is the exact same wall that is in the boys' bedroom.
Continuity mistake: In a first-season episode, Carol is asked by one of her daughters, "How come you never play golf anymore?" indicating she used to play golf. In the later seasons, an episode came out where Carol was first learning to play golf (appearing as if she's never played before).
Answer: The dangling bracelet was used for dramatic purposes - to keep the audience on edge.