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 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.