Plot hole: In this episode Carrie runs into Aidan, who now has what looks to be about a 6 month old baby (Tate). This doesn't seem possible, as Carrie and Aidan would have only broken up about a year ago, and Miranda was around 6 months pregnant when they broke up. Brady is only about 5 months old at this point in the series, leaving Aidan only roughly 8 months to have this baby - but Aidan lay in bed for about a month and then dated Nina Katz for awhile. Timeline just doesn't seem to fit.
Plot hole: When Carrie runs into Aiden on the street, he tells her that he 'married another furniture designer'. Although Carrie is happy for him, it doesn't seem likely that she wouldn't have known about this. Steve and Aiden are business partners and close friends, and Miranda is very close to Steve with their baby. Carrie would have undoubtedly heard about Aiden's marriage through the 'friends grapevine' before that, as news that big wouldn't just slip under the radar. Someone would have told her, so it isn't logical that she is just now finding out about Aiden's marriage.
Visible crew/equipment: When Carrie is entering the NYSE, she has to go through a metal screener. When the security guards are using the wands on her, she spreads her arms, and you can then see some sort of horizontal line or wire sticking out from under her dress, around the waist. There also appears to be something above the wire, showing through the material. She seems to be wearing some sort of contraption under her dress, and when she moves, the entire object moves loosely. Possibly this is her microphone and attached wire?
Continuity mistake: When Steve is wiping Miranda's face with the baby wipes, there are still a few smudges on her forehead. But after she chases him across the room and back again, suddenly the smudges are gone, and her forehead and face are entirely clear of anything. She did not have a chance to wipe her skin at all.