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.
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.
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.
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.

Continuity mistake: In the episode where Big returns from Paris, Carrie meets him at his apartment with a beret and 2 McDonalds bags. She says she got a Big Mac and a Filet O'Fish. She asks him which one he wants, holding the Big Mac in her left hand and the Filet O'Fish in her right. Instantly the sandwiches switch hands in the next shot as Big walks to the right.
Continuity mistake: After Samantha reads Big's birthday note, her cup of coffee swaps between being next to her mouth to flat on the table, depending on the angle.
Visible crew/equipment: During the scene when the four girls are at the bar talking, you can briefly see the boom mic swing quickly overhead at the top of the shot. (00:06:10)

Continuity mistake: After Big asks for permission to smoke his cigar, Carrie's arms are either under the table, or on the table depending on the shot.

The man, the myth, the viagra - S2-E8
Visible crew/equipment: When Samantha is having diner with Ed and she is about to discover what present is under the plate dome, a boom mic is reflected on the silver.

Visible crew/equipment: After Carrie lies to Miranda about getting her teeth cleaned, she turns around and you can see the shape of a square microphone pack through her coat.

Continuity mistake: When sitting at the bar, Samantha points to Charlotte and her date, who are heading up the stairs arm in arm carrying nothing. Yet in the next scene when they arrive at the honeymoon suite, they suddenly have their arms full with a large bag and a basket.
Audio problem: When Samantha reveals her spanx, there is the clear voice of a man (crew) saying something inaudible. (00:11:30)
Continuity mistake: When Big puts his suitcase on the bed, Carrie's left arm grabs a mug to the left of her leg. A shot later it's between both legs.

Continuity mistake: The splattered burger on the painting changes positions between shots.
Continuity mistake: Near the start Miranda opens a book. A second later, from a different angle, she opens it again. (00:05:58)
Continuity mistake: When Miranda is on the street looking for books and meets the reader, the passers-by behind are not continuous. Check the man in a plaid blue shirt.
Continuity mistake: Carrie takes out 2 french fry containers. Then from the opposite angle she takes out one more, but from a wide angle there are only two containers on the counter. (00:19:15)
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