Continuity mistake: At the club, before Sam talks about Mr. Big being "the next Donald Trump," Carrie talks with a guy who places his left hand on his chest. An instant cut later, his arm is lowered.

The agony and the 'ex'tasy - S4-E1
Continuity mistake: In the shower, Carrie wipes the water off her eyes, but a shot later, her arm is lowered.
Audio problem: When Carrie is meeting with Sarah Michelle Gellar and she is told to guess which star is interested in being involved with her project, SMG mouths 'Warren Beatty' and not Matthew MConaughey as is heard.
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.
Visible crew/equipment: When Charlotte approaches Wyle in front of the fire extinguisher, the boom mic is visible at the top of the screen. (00:10:40)
Visible crew/equipment: When Carrie is sitting at the table writing on her laptop after her trip with the girls to the sports bar, the camera comes round and you can see her TV. You can see a boom mic reflecting on the TV screen, and another camera.

Secret sex - S1-E6
Continuity mistake: Samantha and Carrie are hanging Carrie's poster in her apartment. In one shot, the whole poster is pinned to the wall and in the next shot, the bottom left part of the poster is curling up. After another shot of Samantha, the poster is pinned perfectly to the wall again.
Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: When Samantha is talking to Carrie on the beach, Carrie lifts her arm up and places her hand on her head. The reflection on Samantha's glasses show Carrie lowering her arm, but the shot changes back to Carrie and the movement she is doing is not downwards but backwards, leading hear hand to the nape.
Twenty-something girls vs. thirty-something women - S2-E17
Continuity mistake: While talking to her protege, Carrie stubs out her cigarette twice, right before she runs into Big and Natasha.

Continuity mistake: At the beginning of every show we see Carrie walking down the street and she gets splashed by the bus. First the bus has people on it, then in the next shot they all disappear.
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. (00:25:55)
Continuity mistake: In the scene where Carrie and Miranda are eating cakes outside the shop, talking about Miranda having to be supportive to Steve about his basketball competition, keep an eye on Miranda's cake. She takes bites out of the cake and then when it is down to the last bite, the camera shows Carrie, then shows Miranda again with the cake suddenly full.
Valley of the twenty-something guys - S1-E4
Continuity mistake: Carrie receives a phone call from Samantha and her voice over says she needs her morning Marlboro Light, however, when she picks up her pack of cigarettes, you can see that it is a pack of Merits.
Continuity mistake: At the furniture show, when Carrie is introducing Big and Natasha to Aiden, Carrie accidentally spills her coffee on Big. A coffee spot that splashed on Carrie's upper blouse keeps appearing and disappearing throughout the scene.
Twenty-something girls vs. thirty-something women - S2-E17
Deliberate mistake: In the scene at the beach party, when Carrie brings everyone beers, Miranda says "There's so much foam, I could ski on the head," but the cups are tipped toward camera and you can see there's no foam at all.

Attack of the five foot ten woman - S3-E3
Continuity mistake: The episode 'Attack of the 5 foot 10 woman' in season three, when Charlotte is afraid of the sauna. She is running into the sauna with a towel wrapped around her waist. The towel comes loose and is nearly falling off - but in the next shot it is neatly tied around her waist.
Twenty-something girls vs. thirty-something women - S2-E17
Visible crew/equipment: A white screen and crew member holding a boom mic are reflected in Samantha's glasses when she is talking to Carrie on the beach.

Oh come, all ye faithful - S1-E12
Visible crew/equipment: When Charlotte visits the psychic who tells her that she doesn't see marriage, a boom mic moving around is visible at the top middle of the screen, when the psychic is in shot.

Continuity mistake: In the opening credits, when Carrie gets splashed by the bus, her pink tanktop changes from slightly wet to soaked in half a second.
Answer: I'm a long-time fan of the show, having re-watched it many times, and I definitely remember slightly different dialogue at the end of that episode than what's on my DVD. I'm afraid I have no idea why this change might have been made or any other info, but you're not insane.
Purple_Girl