Revealing mistake: When Carrie bumps into Mr. Big and her purse falls, watch the people in the background carefully. Many of them are watching the couple talk and interact with each other. On a busy New York street nobody is going to pay attention to two people having a conversation. Apparently all these people were watching the shooting of the scene.
Continuity mistake: While having coffee with Carrie, Skipper cries "I hate that word!" and raises his hands next to his head. A shot later they are not close to the head.
Continuity mistake: When Miranda is drinking with Skipper, she brings her cocktail close to her face twice.
Continuity mistake: Charlotte gets in a taxi with his date and the cab drives fast and leaves. Inside the cab, it drives really slow. It even gives the impression of being still for a couple of seconds.
Continuity mistake: When Sam is smoking a cigar with Big, a woman suddenly appears right behind her.
Continuity mistake: After Carrie has sex, Kurt's grey underwear way below his groin (to protect his modesty) is briefly seen. (00:12:16)
Other mistake: When Carrie opens the newspaper to read her column, the same paragraph is repeated at least twice.
Continuity mistake: When Miranda recalls the Linda Fiorentino movie, Carrie's right arm swaps between holding a cocktail or resting empty handed by her lap.
Continuity mistake: When the couple is practising golf, the sky has dusk light, but in the immediate shot it is bright blue.
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