Continuity mistake: At the end of the show, when Carrie visits Jeremy at the psychiatric facility, they are sitting outside having a picnic. As they are talking, notice Carrie's necklace. It is a bolero-type necklace and the red stones on the end move up the necklace to near the clasp and then back down into her cleavage. Then they go back up again.
Revealing mistake: When Jeremy comes to visit Carrie at her apartment, he is wearing a white polo style Lacoste Izod shirt. There is a noticeable rip or small hole in the upper shoulder of the shirt, visible on screen. This was intentional by the wardrobe department. They wanted to show that despite Jeremy being an older, Ivy League kind of guy, he came back still dressed similar to how Carrie would have seen him in high school.