Continuity mistake: When Carrie and Shaun are laying on the floor of her bedroom, she has her left hand resting on her chest. But in the very next shot; her left arm is laying across her stomach, and her left hand is curved around her right waist. No time has passed in between these shots.
Continuity mistake: During this scene when Samantha is confronting her new assistant, the office set-up is completely different than before, when Nina G. was working for her. The assistant office space is much larger, glass desk, different angle, next to small conference room instead of Samantha's office, etc.; obviously not the same office set as previously used. Yet Samantha has not changed offices at all during this time period, as it wasn't too long ago when she fired Nina G. Something as major as changing offices would definitely have been mentioned in the plot (as changing apartments always is); and there hasn't been enough time since she fired Nina G.
Character mistake: When Carrie is describing the younger guy she is dating, she claims he is the creator of an Internet magazine 'that she still wasn't able to find on her computer'; meaning she had searched the Internet for it. But as we learn later in the series, right before she gets back together with Aidan for the second time; she doesn't have the Internet on her computer until then. The girls talk her into getting it, in order to email Aidan. So there was no way she could have searched for the other guy's Internet magazine on her computer, as it was an older Mac laptop and not likely to have search engines without Internet access. She was only using the hard drive at that time.