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.
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: In the courtroom, as Carol is giving the judge her side of the story, she's looking in the direction of Mr. Duggan the whole time while saying "otherwise he wouldn't have hit me." Then the camera changes angles and instantly Carol is turning from facing the judge back towards Mr. Duggan.
Continuity mistake: At the start of the episode there's a wide shot of the house exterior as the Brady's station wagon is pulling into their driveway, and the wagon has wooden side paneling, but in the next closeup the paneling is gone. Plus the fact that the rear-end damage doesn't exist in the first wide shot, which is the point of this episode.
Continuity mistake: During the recording of "Time To Change", Jan's hands are always together when she's shown. But in the shots showing just the boys, look at the right side of the screen and you can see fingers (which have to be Jan's since she's standing beside Peter) moving as if they're drumming on something.