Babysitters' Island Adventure centers on Dawn and Claudia being stranded on an island with some kids (including Dawn's younger brother Jeff and little Jamie Newton), Claudia reveals some quick thinking when getting everyone to safety and manages to keep calm and take care of little Jamie when he gets a high fever. Dawn later says that she can't imagine what she'd do without her.
Claudia meeting her idol, solving the mystery, and getting her dream museum job at the climax of Claudia and the Mystery at the Museum.
Even better; right before that, Kristy, known for her skill in all things athletic, tries her hand at the pie throw and fails miserably.
Slightly inspired by Taming Of The Shrew, Stacey decides to use "reverse psychology" on the snotty and bratty Delaney children. In a bid to get the children to start cleaning their toy room, Stacey starts throwing more toys on the floor because they claim to like the room messy. Then when the son demands milk because he's thirsty (with no please), Stacey then suggests she'll get some other beverages and starts removing several glasses and setting them after being demanded to "pour". She manages to get the daughter to pour just 2.5 glasses of milk. Then plays them into cleaning up a spill by insinuating that they like her to clean things up and and that she can give them a bath. She tells them also "I would feel very, very sorry that you are eight years old and unable to get cookies yourself" after answering the daughter's question of what Stacey would do if they demanded cookies. Then she showed them how to play "Snail". The Sitters get hired again and manage to discipline two brats.
At the end of the book, Kristy is stunned when the Delaneys demand that Shannon Kilbourne (their regular sitter for years) get them a drink. All Shannon has to do is raise her eyebrow, and they meekly get it themselves.
The first book has Claudia managing to gain control of Jamie Newton's 3 bratty cousins (which includes a He-Man Woman Hater in training) in one night, they ended up having a quiet story time.
The second time she's asked to sit for Jamie's cousins, Claudia insists on bringing Kristy for backup. Kristy gains control of them with an ear-piercing whistle. The aforementioned boy on the brink of his girl-hating phase is so awed by this that he wants Kristy to teach him and he behaves the rest of the evening.
The 3rd book has a verbal showdown between the fledgling BSC and their competition, a group that hires both older girls and boys, comparing who has more knowledge of their client's children and calling them out for the irresponsible and self-absorbed sitters they've hired (one of whom let out a coatless Jamie Newton to play in the snow unsupervised and another who smoked while sitting and burnt their cigarette on a client's cushion). The titular club proves that they may be very young, but they are truly competent and caring.
Claudia and the Terrible Truth has Claudia babysitting for a seven-year-old and five-year-old whose father is abusive. She is extremely compassionate with the kids, as are the other baby-sitters. It also takes bravery for Claudia to approach her mom for help, especially in a universe where adults are not consulted as much as they could be. Finally, Claudia is shaken but remains cool-headed after the dad calls her private number, demanding, "Give me back my wife!" (The mom had, by then, taken the kids to her sister's home in New York.)
During Claudia Kishi, Middle School Dropout, Claudia is sent back to seventh grade because of her poor grades. She's naturally depressed and discouraged, but meets a local artist who encourages her, explaining that she went to college and achieved fame even though she was held back three times.
In Keep Out, Claudia!, the Lowells request that Claudia no longer sit for them, then turn Jessi away at the door when she goes instead. They also forbid their kids from participating in a concert with songs from Fiddler on the Roof, assume Mallory is Catholic, and some other small incidents lead the sitters to realize that they're pretty racist. When the mother calls and asks for a "blonde-haired, blue-eyed" baby-sitter they'd heard about, both Stacey and Dawn refuse the job, so Kristy gleefully calls back, telling her that they're fresh out of blonde-haired, blue-eyed babysitters, but she'd be happy to sit for them if she's not busy taking care of her Vietnamese sister... she's promptly hung up on and declares they've lost a client.
For readers who don't like Kristy, or consider the entire series Snark Bait, Stacy's falling-out with the club in Stacy vs. the BSC qualifies as this. Before quitting, she gives Kristy a "The Reason You Suck" Speech that's actually pretty accurate.