Continuity mistake: When Carrie exits the Wall Street subway station, the passers-by on the right are not continuous between shots.
Continuity mistake: When Carrie bumps into the dogs, the dog walker is sometimes on the middle of the streets, others next to the building, others crouching and others standing still. No continuity. (00:01:05)
Continuity mistake: When Carrie is running, the dalmatian is on the right side of the curb. A shot later it's on the left.
Continuity mistake: When Carrie runs late there's a man with a hat next to some flowers half a meter away. She keeps running and the man vanishes, only to reappear seconds later.
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. (00:06:55)
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? (00:02:40)
Answer: A popular brand of sexual lubricant. See http://www.k-y.com/index.jsp.
J I Cohen