Revealing mistake: When Carrie bumps into Mr. Big and her purse falls, watch the people in the background carefully. Many of them are watching the couple talk and interact with each other. On a busy New York street nobody is going to pay attention to two people having a conversation. Apparently all these people were watching the shooting of the scene.
Continuity mistake: When Carrie arrives backstage at the fashion show, she's wearing a black dress with a long jewelled necklace that is wrapped once around her neck and hanging down on both sides of her chest, like a scarf. When the fashion show starts, the necklace strands are tied together in a big knot/wrapped around her neck more. Then, when she's about to get in a cab home, they are untied/hanging down again.
Continuity mistake: When Big arrives at the party Carrie is eating a snack, with a remaining one on her hand. Big sees her and she's eating another snack, which leaves her with zero food. Half a second later there's a wide shot and not only is she not chewing the previous bite, but 2 snacks have suddenly appeared on her hand.
Visible crew/equipment: When Stanford and Carrie walk backstage with the models, check the reflection on the glass and you'll see: the boom mic operator, camera and, best of all, a group of technicians crouching on the floor, failing to hide and moving around when Carrie and Stanford walk around.
Continuity mistake: Before dinner, Miranda holds the candles with her right hand. Then puts them in her left hand. A nanosecond later, from a different angle. She is leaving them on the table using her right hand. She couldn't have used her left hand for she is holding the napkins and they would've fallen down.