If you slow down the video as Carrie drops the pie pan it never touches the back of her legs yet she rubs the front & back of her legs as if they were both burned.
Willow Summers, the movie star that Big is dating, is obviously fictitious- but it's possible that this was a portmanteau of two characters names from Buffy the Vampire Slayer, Buffy Summers and Willow Rosenberg.
At the end Samantha kicks her leg out to get a cab. Carrie does it in Abu Dhabi, when they're trying to get to the airport in Sex and the City 2. She was mimicking Claudette Colbert from It Happened One Night which she & Big watched after Stanford & Anthony's wedding.
The Frozen Cup where she goes for a meal in "New Jersey" is really an only ice cream place on long island Nassau/queens border in New York.