Plot hole: After dinner, Carrie is using her computer when Aiden suddenly is shown logging onto her AOL Buddy List. (Upper right of her computer screen). Since Carrie is unfamiliar with AOL, the Internet or how to use the Buddy List features, it's unlikely she would have already added Aiden ("AidenNYC") to her Buddy List. And you have to manually add someone to your Buddy List, it doesn't just automatically appear when you use email. But since Carrie apparently doesn't have any idea how the Buddy List/IM system works on AOL (according to her trying to 'hide' from it); she wouldn't have thought to manually add Aiden to the Buddy List at this point. It doesn't make sense.
Plot hole: When Carrie is sitting on the kitchen table after Aiden ices her legs, they begin to kiss. As they lean back over the table; Carrie stretches her legs out and wraps them around Aiden, rubbing them against him several times. She has just been painfully burned on her legs, but suddenly has no problem rubbing the burned areas against his waist without any pain, problems or hesitation. She is acting as if she was never burned; but the skin would have still been tender, and it would have hurt to brush it against Aiden in that manner.
Plot hole: When Carrie sits down to read Aiden's 'farewell letter,' she discovers he has left her legal papers instead. Miranda later examines the legal documents, and explains the terms at the restaurant. But Aiden has only just moved out that day, and had spent the previous night in the apartment next door. (This was made clear in the previous episode, when Carrie explains in voiceover that 'the next day, Aiden moved out'.) He has spent the day moving his things out; there is no logical way he would have had time to contact a legal firm, make an appointment, go to the appointment, make arrangements to deal with Carrie's apartment, and have complex legal documents drawn up and ready to give to Carrie. None of this could have possibly happened between the night before when Aiden decided to end the relationship, and the next day when he physically moved out. No additional time has passed, as Carrie asks him to stay 'one more day', implying this really is the day after the previous episode.
Plot hole: When Aiden suddenly shows up below Carrie's window the night of their dinner together, she gets up and looks down at him from her apartment. He suddenly starts to run into the building, and at the same time Carrie immediately starts running quickly through her small apartment to get to the front door. It would have only taken Carrie a few seconds to get across her apartment, but Aiden would have had to run up the three or four flights of stairs to reach the front door of Carrie's apartment . That would obviously have taken much longer; yet as soon as Carrie opens the door, Aiden is already there and running into the apartment.
Plot hole: When Charlotte places her ring box in front of Carrie on the table at the restaurant, there is a close-up shot showing that she is still wearing her simple gold wedding band on her right hand. The entire episode has emphasized that it's strange for Charlotte to still be wearing her diamond engagement ring when she is alone, since she is getting a divorce. So why is nothing mentioned about her continuing to wear her gold wedding band? That doesn't seem to be an issue, but wouldn't it be just as strange?