Happy Birthday and Too Many More - S3-E15
Other mistake: Laura is doing some work on when to have Richie's birthday, and Rob tells Laura "I thought we decided that about 8 years ago." Yet Mrs Billings has asked Rob to do 2 plays (1 each year for the PTA meetings) In the Happy Birthday... (Feb 1964) episode that would have made Richie about 10 due to the fact that Richie was 8 when "What's in a middle name" (Nov 1962) aired. (00:01:00)
The Ballad of the Betty Lou - S3-E9
Other mistake: While Jerry and Rob are furious, Jerry asks the sailor "What's the matter with the lights?" and the sailor says "power failure on the line, they can't locate it." If there's a power failure then the room would be completely dark just like it is outside. Yet Rob and Jerry have shadows on their hats, jacket, shirts etc. as well as a shadow from the bunk bed. These shadows are caused by the non-working lights or the lights behind the camera.
What's in a Middle Name? - S2-E7
Deliberate mistake: Rob, Sally and Buddy's "old office" is exactly the same shape as Robs basement (except for the door in the center of the back wall. Instead of going upstairs it's all on 1 level. There's a door to the right which goes into a random room which we never get to see inside). (00:10:38)
Suggested correction: Since you listed multiple differences, it's obviously not "exactly the same." Filmmakers not building every set and prop from scratch is not a mistake. Modifying and reusing old sets is just an economic reality of production. If anything this should be under trivia.
The Brave and the Backache - S3-E19
Other mistake: When Rob goes into the office of Dr. Philip Nevins there's smoke rising from the ash tray on his desk. Throughout the scene nobody's smoking.
Three Letters from One Wife - S4-E10
Factual error: Millie mails 14 letters to Alan Brady with names of dead relatives, and to give them different postmarks she says that she drove all over Westchester and southern Connecticut to mail them. The next day, all 14 have arrived. Mail crossing a state line would not likely have made it overnight.
A Man's Teeth Are Not His Own - S2-E13
Factual error: Rob is in the middle of eating a sandwich. You can't break a tooth on a sandwich unless it's frozen, cement, glass or made of ice.
Suggested correction: Rob specifically said he broke the tooth on a chicken bone that was in the sandwich.
The Great Petrie Fortune - S5-E6
Revealing mistake: The great-grandfather Petrie was just Rob Petrie dressed as a really old man. The lamp in the movie is also one that has been in Robs house and Sally's house in a few of the episodes.