Continuity mistake: In the scene in the kitchen with Val, Fran takes two green cups and places them on the bench. She takes two teabags and places them in the cups. In the next scene the two cups are on the table with Val, and Fran carries the teabags over to them and puts them in.
Other mistake: Pretending to be Max's assistant, Fran dials a number for Bernadette Peters. The conversation is on speaker phone. The assistant says "one moment please." Niles and Fran continue talking and Maxwell comes in. Fran and Niles sheepishly hurry out of the room. Notice how, this whole time, Fran never touched the phone again to turn the phone off. So Max would hear Bernadette Peters and actually figure out Niles and Fran's plan before the episode's even halfway over.
Continuity mistake: In the scene where Val and Fran are in the kitchen, Fran jiggles her tea bag, the removes it and places it on the napkin beside her. Brighton enters and after a brief conversation Fran returns to the table carrying cream and sugar. She then jiggles and removes the teabag from her cup again.
Continuity mistake: In the opening sequence, Fran arrives at the Scheffield house with a case of make-up. When we see a shot of the makeup head on, one can see two lipsticks at the far left corner of the case. When we see a shot of the case from behind, the lipstick is now at the right corner of the case.
Continuity mistake: None of the Sheffield children are aged properly over the course of the series. It's established that Grace is 6 years old in season 1, but two years later in season 3 she's 10. Maggie is 18 at the end of season 5 but turns 21 years old in early season 6. And finally, Brighton is in seventh grade in season 2 and somehow is graduating high school at the end of season 6 (when he should be only a junior, and nothing about Brighton's character would suggest he's capable of skipping a grade).
Continuity mistake: In the kitchen at the beginning, Fran pours milk into three glasses. After she fills the third glass, she starts to put the milk down. In the next shot, she is holding the bottle up to the glass again and pours some more milk before putting the bottle down.
Continuity mistake: In the first office scene, when Fran picks up Allan Beck's resume and pages through it she is holding the pages in the middle. When the shot changes to Maxwell and he says "Yes, but I'm still flammable", watch Fran's hands in the corner of the screen. She's holding the pages by the corner.
Other mistake: About 2/3 into the show, Fran carries a box of cookies into Maggie's bedroom. The box's name brand is covered over but Fran says she brought the Mallowmars. However when they show an actual cookie they are eating, you can see it's a Snackwell Devil's Food Cake cookie, not a Mallowmar.