Deliberate mistake: The second time they show Samantha having sex on her 'rolling bed', you can see that the guy is too far above her to actually be having sex with her. They are too far apart, probably to make it less awkward for the actors. (00:12:05)
The big time - S3-E8
Continuity mistake: When the girls are in the bathroom talking about their periods and doing their make up, we see Carrie remove the hair scrunchie from her wrist with her teeth twice, once in the mirror in a shot from behind, and then again from the front.
Plot hole: After Carrie misses the Staten Island Ferry, Bill Kelly suddenly drives up in his own car to offer her a ride home. She accepts, and gets in the car. He then asks her 'how do they get off the island' as if he has no idea of what roads to take. But he has obviously driven his own car TO Staten Island, so he should know the way back. (00:27:50)
Continuity mistake: During this scene when Samantha is confronting her new assistant, the office set-up is completely different than before, when Nina G. was working for her. The assistant office space is much larger, glass desk, different angle, next to small conference room instead of Samantha's office, etc.; obviously not the same office set as previously used. Yet Samantha has not changed offices at all during this time period, as it wasn't too long ago when she fired Nina G. Something as major as changing offices would definitely have been mentioned in the plot (as changing apartments always is); and there hasn't been enough time since she fired Nina G. (00:13:45)
Suggested correction: You're assuming that moving to a new office must be a plot for a new episode, which makes no sense (plus, it's a show that revolves around sex, women, restaurants and bars). Furthermore, the episode you mention is S2E17. Many months have passed and it's perfectly plausible for Sam to move some place else.
Continuity mistake: When Carrie is lying on her bed, she is wearing yellow pants over a green top. The top portion of her pants is unbuttoned/unzipped as she moves. But after she picks up the phone to call Big, she is sitting up on her bed, and her pants are suddenly buttoned/zipped completely up. There was no opportunity in this sequence for her to have closed her pants. (00:12:15)
Revealing mistake: When the transvestite is throwing eggs at Samantha's window, she is holding the cardboard egg container in her left hand. She keeps throwing eggs, but you can tell by the way she is holding the egg container that it is really empty. It flops down vertically from her hand, and there is no way eggs would be able to remain in the egg crate by holding it in that manner.
What goes around comes around - S3-E17
Revealing mistake: When the gardener hands Charlotte the rose, he is supposedly picking it out of some rose bushes he is in the process of planting. He even makes a motion as if 'picking' it from the bunch. But when he hands the single long stem rose to Charlotte; it's obvious that this rose has already been cut, and is missing the lower leaves. (00:16:05)
Revealing mistake: When Tray and Charlotte stand by Tyffany's door, bystanders on the right and on the left sneak-in to see the filming.
Revealing mistake: After Carrie leaves home because Aidan is fixing the floor, Charlotte and Trey walk down the street. There's a group of people on the left who can't stop looking at the camera.
Continuity mistake: When Steve arrives at Miranda's place he cuddles the puppy, but his left hand's position is not continuous between shots when he thanks her for sleeping on the couch.
Audio problem: Sam asks the waiter how long does the wheatgrass take to work into one's system, but the last sentences are played with a side shot of her where she's not mouthing the lines.
Continuity mistake: When Carrie debates with Miranda whether to call Big or not, Carrie holds the pillow close to her chest in one shot, but over her thighs in the other.
Continuity mistake: When Carrie says Aidan is a good man she places her hands on his face, but his collar gets stuck in between. From a different angle the collar is several inches below.
Revealing mistake: When Trey and Charlotte stop in front of Tiffany's, all of the passers-by stare at the camera. There's even a bald man in a white T-shirt who stops dead in his tracks and sneaks his head in between Charlotte and Trey while staring.
Continuity mistake: During the party, when the music starts the man with white bermudas and light blue shirt behind Charlotte keeps changing positions between shots.
Continuity mistake: In the duck pond, Big's wet hairstyle changes between shots. Also Carrie's, from soaking wet and straight to slightly curled.
Continuity mistake: After Trey and Charlotte have sex, the way his jacket lies on the box changes between shots.
Continuity mistake: At Charlotte's, Sam reaches for the Martini on the fireplace and turns around. A shot later she is reaching again for the Martini and turning around again.
Continuity mistake: Carrie places a thick blue book on the right side of the fireplace, but a shot later it appears on the far left side.
Continuity mistake: While unpacking at Charlotte's place, she holds one candle in one shot, but they suddenly become two a second later.
