Continuity mistake: When Mr. Dittmeyer is sitting on the toilet, just before the floor collapses, when seen from his point of view, there is a lot of debris and other objects around the base of the toilet. From the wide shot, when the floor collapses, most of the objects are gone.
Deliberate mistake: In the Search for the Stars contest, at the end of the song their mouths have stopped singing as they go to bow but you continue to keep hearing them apparently sing a few seconds longer as it fades out. This is a joke referring to the original Brady Bunch episode where the kids sing the song on live television and the song similarly fades out after they've stopped singing.
Revealing mistake: During the scene where Mr. Dittmeyer is standing in front of the 9 TVs, you can see that the middle 3 people (Mike, Carol and Alice) are all taken from the same camera/angle as they all have the same background. As such that would then mean they were recordings being played back vs. being live shots as beginning of the musical number portrays.