Other mistake: When Sylvia is outside the Sheffield mansion she says "I wonder if my daughter Fran is at home? I will see if she is" the doorbell rings as soon as she finishes that line, but you can see both her hands are visible. She can't have rung the doorbell.
Other mistake: In some episodes, there is a small room between the kitchen and dining room (the "Butler's Pantry"), but in other episodes the same door leads directly into the dining room, and in still others it leads into a passage.
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.
Smoke Gets in Your Lies - S1-E2
Other mistake: Fran and Maxwell come out of the dining room and go into the living room. They come out of the door that normally leads to Maxwell 's office.
I Don't Remember Mama - S1-E22
Other mistake: Towards the end of the show, Fran has a tape of the Sheffield's which she removes from the cover and inserts into the player, upside down. It's quick but it's there. (00:21:30)
The Nuchslep - S1-E4
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.
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.
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.