I remember being vaguely repelled by the manicures in MM, precisely, I think, because we’re supposed to be.
Consider Betty Draper’s hands in an early episode when she loses control of the steering wheel or can’t apply her lipstick: her clumsiness indicates her repressed frustration over her status as Don’s wife, and her awkward manicure punctuates that thought.
Indeed, Betty’s nails seem like artificial appendages that get in the way of everyday activities. She doesn't even eat supper with the family, smoking and drinking instead, as if managing a knife and fork is simply too difficult. Note, too, how her long nails curl up a little at the end, suggesting their inappropriate fit on her hands, the poor fit of her character to her life.
There’s also Glenn’s mother, who has long, red pointy nails, which, ahem, point to her being marked as a divorcée, a woman whose selfish actions threaten the other wives (could she have designs on their husbands?).
The manicures of the other female characters didn’t leave an impression in my mind. But if I were to follow Bazaar’s advice to emulate a Mad Men manicure, I might cheekily look to Betty’s hands when she’s shooting at the birds. In this moment of inspired Hitchcock one-upwomanship, Betty’s manicure is tellingly all but invisible as she finally asserts her authority.