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 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?