Factual error: When the hot air balloon comes down with Carrie in it you can see N410AA printed on it. This is commonly called a tail number on planes and is issued through the FAA, which of course did not exist during the time period of the episode.
The People vs. the Fonz - S11-E11
Factual error: When the Cunninghams are talking about Fonz's trial, Mr. Cunningham can be seen wearing a digital watch. Digital watches didn't exist in the 50's.
Suggested correction: Wasn't Mary the one in the balloon?
Mary was in the balloon earlier in the episode with the man who runs it but near the end, Carrie wondered off into it and it took off with her inside ALONE.