Love is a Many Blundered Thing - S3-E19
Continuity mistake: Watch Brighton's arms in the opening scene in the Kitchen. The banana he is holding and his arms move positions between shots.
Continuity mistake: When Sylvia comes in and wakes Fran, she puts her hands on her Hips when she says "grow old with dignity", and when the shot changes her hands are at her sides.
Continuity mistake: When Maxwell shakes Fran awake the first time (in her dream), his hands are on her shoulders. When the shot changes his hands are suddenly on her legs.
Continuity mistake: When Fran is trying on her shoes in the shoe shop, her legs are crossed. Then in the next shot they are instantly uncrossed and she stands up.
Character mistake: While driving in a taxi, Fran says McDLT was discontinued in 1994, but in fact it was three years earlier in 1991.
Continuity mistake: Just before Fran opens the door for her date, her handbag switches hands between shots when she says, "It's cuter on me."
Factual error: Fran is dating a hockey player who plays for the New York Rangers by the name of Michael LaVoe. He wears the number 7. The number 7 is retired by the NY Rangers, it was worn by Rod Gilbert.
Continuity mistake: In the dining room during breakfast, while Fran is talking, Niles starts to turn away from the window towards Fran with a teapot in his hands. When the shot changes he is facing the window again and turns around with the teapot a second time.
Continuity mistake: When Fran and Val are in the sports bar in the beginning, the popcorn in their hair changes between shots. This is especially obvious on Val.
Continuity mistake: When Fran is discussing why she never studied tennis she is eating a celery stick and using her right hand but when we see her in the next shot she is eating a carrot stick and using her left hand.
Continuity mistake: When Fran's date Jack first enters the house, Fran closes the door behind him. A couple of shots later, the door is open and Fran is closing it again.
Continuity mistake: In the scene when Fran is having an intimate talk with Joan, Fran has a cookie in her left hand. Next scene it's an empty glass which she then pours a drink into, then the glass is empty and Fran again fills it. (00:14:10)
Other mistake: In this episode, Maxwell finds out about Fran's tattoo. Fran mentions that her tattoo was on her behind. Maxwell spends the episode trying to see it but in Season 3 and Episode 26, when the Sheffields are in the beach, Fran strips down to her bikini in front of Maxwell. Maxwell checked her from behind, meaning he should have been able to have seen her tattoo.

Danny's Dead and Who's Got the Will? - S4-E12
Continuity mistake: At the start, when Fran joins Niles, she's holding a green mug in her left hand and a muffin in her right hand. But the mug and muffin suddenly switch hands when Fran and Niles head to the sofa.
Character mistake: The Sheffields are going to Miami but when they are there, Maxwell mentions having gone to Disney World on the same trip. Disney World is not in Miami, it's in Orlando.
Continuity mistake: When Fran's in the kitchen making an ice cream sundae she tops it with a lot of whip cream, but after Fran pulls a tissue out of Gracie's shirt, when she and Maxwell sit down all of the whip cream suddenly vanishes, but then it reappears.
The Bobbie Fleckman Story - S5-E3
Visible crew/equipment: During the videotaping of the Brian Setzer Orchestra in the Sheffield home, some of the camera angles (not the norm) are so low that we can see the top of the set.
Continuity mistake: When Mr. Sheffield is running towards the van to rescue Fran and Val, the kidnapper is watching him through binoculars but is looking through a window in the opposite direction that Mr. Sheffield is actually coming from. Mr. Sheffield is coming up the back and the guy is looking out of the side towards the front of the van but is still telling the girls what Mr. Sheffield is doing.
One False Mole and You're Dead - S5-E12
Character mistake: CC, when talking about the Marie Antoinette show, says that Louis and Marie had two children. They actually had four children (Marie Therese, Sophie, Louis Joseph, and Louis XVII).
Answer: Mr. Sheffield needed someone to manage the kids, not necessarily babysit them. Brighton was a Bart Simpson type, Maggie was shy and awkward and Gracie had personality issues.