Plot hole: Lots of factors here: The doctors end up with the opposite kids that they were supposed to have... Why didn't they simply switch in the first place rather than go through all the drama? Also, the male doctor admits Alice let him in and most likely Alice would have told him first door on the right (like she's given directions in other episodes) to locate Peter. And the biggest question of all is, what doctor would make a house call and not look for their patient rather than just ending up with someone else they were not called to see (remember, each parent called their own doctor to see their biological kid).
Plot hole: Peter thinks he has a fatal disease. The parents realise two pages stuck together and he went from page 95 to 98 mistakenly. However, Mike first read about the actual fatal disease info on page 97, and then Carol read about what Peter actually had on page 96 (poison ivy). If Peter read only 95 and 98, there would be no way of Peter to know his disease was fatal since that was printed on page 97.
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.
Plot hole: The Bradys and Alice run a relay through the amusement park to get the sketches to Mike at the manager's office. They locate another person to pass the cylinder off to when they get too tired to run. But they all arrive together seconds after Carol gives the sketches to Mike. (00:19:15)
Plot hole: When Mike was at the meeting and pulled out the Yogi Bear poster, he said he could find the other cylinder, and was told by one of the other men that they had to catch a plane in 30 minutes. After that, he had to find Jan, and then Jan and Marcia had time to go on about 4 rides and then find the sketches and then start their run across the park. There is no way all of that could have been done in less than 30 minutes.
Plot hole: Greg Brady is suppose to be under 21 so he can't legally sign any type of contract, also at the end he rejects his new persona and tears up the contract. Tearing up a contract doesn't nullify it.