Other mistake: After Jack leaves the apartment with Mr Angelino, Janet and Terri are sitting on the couch trying to figure out a way to get money for Jack. When Janet gets up you can see the bathroom door start to open behind her but there is no one else in the apartment to open it.
Character mistake: Maria (Felipe's cousin) supposedly didn't understand any English (only single words like "yes") and would answer (in Spanish) "Que?" after a full sentence of English was spoken to her. However, in front of Jack, one of the girls said to Maria "Tell Jack the new English word you just learned" and Maria understandingly responded "No." There's no way that Maria could respond correctly to that question since she didn't understand any other English sentences throughout the episode.
Revealing mistake: As Terri exits Jack's bedroom to stall the diamond thieves, you can momentarily see into the girls' bedroom. The wall that should be between the girls' bedroom and Jack's bedroom is missing and the floor and blue curtains of Jack's bedroom set are visible. Someone's arm wearing a light colored shirt (John Ritter's sleeve is brown and Joyce DeWitt's sleeve is black) can also be seen moving.