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 opening titles sequence, cartoon Fran is thrown out of the bridal shop and the doors are closed behind her. When she hails a taxi in the next shot the doors are open 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.
Pilot (a.k.a. The Nanny) - S1-E1
Continuity mistake: When Maxwell comes over to Fran's mom's apartment he sits on the couch. There is a orange pillow behind him and a yellow pillow next to Fran. Part way through the scene the yellow pillow is now behind Maxwell.
Pilot (a.k.a. The Nanny) - S1-E1
Continuity mistake: After Niles walks into Maxwell's office, C.C. puts her hands on the chair Maxwell is sitting on. When Maxwell says "Yes Niles what is it?" the shot changes and C.C.'s hands are no longer on the chair.
Smoke Gets in Your Lies - S1-E2
Continuity mistake: When Val comes over and sits on the couch she crosses her legs. The shot changes and she crosses then again.
Continuity mistake: The smash vase is placed on the office desk by Niles, it keeps jumping back and forth between two different orientations between scenes. (00:10:34 - 00:12:57)
The Nuchslep - S1-E4
Continuity mistake: When the Chinese food is delivered, Fran's hair is very flat and the curls are loose. In the next scene, she goes to talk to Maxwell and her hair is noticeably curlier.
Continuity mistake: When CC and Maxwell arrive at the wedding, CC has no scarf around her neck. When the scene cuts to her shortly after arriving there is a large brightly-coloured scarf around her neck, and two shots later it has disappeared again.
Continuity mistake: In the dining room, CC is wearing a scarf over her head as part of her "safari" outfit. When the shot shifts to a close-up of her looking horrified at the thought of taking the kids to the Zoo on her own, the scarf is suddenly around her neck.
The Butler, the Husband, the Wife and Her Mother - S1-E6
Continuity mistake: When Sylivia is telling Fran about her birth, she raises her right hand and has her left hand on her hip. When the shot changes her left hand is raised and her right hand is on her hip.
Continuity mistake: When Fran and Gracie are making cookies there is a spatula on the cookie pan that changes position a couple of times throughout the scene.
Continuity mistake: In the kitchen, while Fran is telling Maxwell about Brighton and Tiffany in the shower, the glass of juice on the counter appears and disappears between shots.
Continuity mistake: When Maxwell is talking to Brighton about the battle of the sexes, he puts his hands in his pockets. The shot changes and suddenly his hands are at his sides and he puts them in his pockets again.
Continuity mistake: When CC takes the pile of showgirl resumes from Maxwell in the office, she holds them with both hands. When the shot changes, she is holding them with one arm under the pile and the other hand leafing through them.
Sunday in the Park with Fran - S1-E18
Continuity mistake: When Fran is sitting at the table with Grace when C.C. is on the phone, the coloring book in front of Grace is open. Fran goes to pick it up, the shot changes, and Fran has already picked it up.
Sunday in the Park with Fran - S1-E18
Continuity mistake: When C.C. is trying to get Grace to play with the son of the Broadway critic she is coloring with a green crayon. Near the end of the scene it is suddenly a red one, and the paper she is coloring on is all red with no green so she could not have changed colors.
Continuity mistake: In the second gym scene, while Fran is talking to The Gym Teacher, Maggie's arms change from being crossed to hanging at her side between shots.
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.
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.