Continuity mistake: In "Our Son, the Man", Greg wants his own room. One night, while in bed, Mike and Carol discuss their options. Carol says, "How about the attic?" Mike responds with, "That would be fine if Greg were only two and a half feet tall." Later, they give Greg the den for a while. However, in "A Room At the Top", after cleaning out the attic, which was now full size, both Greg and Marcia want it for their own private room.
Other mistake: A final contest is given for control of "green stamps" with all the kids building a "House of Cards." Whomever causes the cards to fall will be the losers. All is going well until Tiger comes in and knocks into Peter and causes him bump the table and knock over the cards. If you watch closely at the end of the scene, when all the dialog is finished, you can see Mike trying to knock down a few remaining cards. However they keep popping up. Probably due to the fact that the cards were glued together to make it easier for the kids to build upon.
Continuity mistake: When the vase gets broken, it's easy to see that one large piece flies off the chest of drawers onto the floor. And when the boys look down at the broken vase from upstairs, three pieces are on top of the chest of drawers. But Greg - seen later trying to fix it - says something to the effect of "Good thing it only broke into three pieces." So what about the piece that flew off onto the floor?
Continuity mistake: When the kids are building the card castle to see who would get to choose what they get with the stamps, Jan is putting a card on, in one shot her hair is up in a ponytail then in the other shot her hair is down. This happens back and forth when the shots change.
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.