Continuity mistake: There's a scene that opens with Carrie and her boyfriend in his apartment, and he's sitting with baby Brady on his lap. The camera cuts to another angle, and it's very obviously a different baby.
Out of the frying pan - S6-E16
Continuity mistake: The dog owner says the dog is a looser "and it's a shame", while Charlotte's left hand covers the dog's body. A shot later it's just over the dog's front leg. (00:10:45)
Out of the frying pan - S6-E16
Continuity mistake: When Charlotte introduces herself to the dog owner, the dog's head looks at a different place in every single shot.
Out of the frying pan - S6-E16
Continuity mistake: When all four girls are having Manhattans, and Miranda recalls an awful apartment she had, Sam's arms are under the table or on top, depending on the shot. Also, her purse appears and disappears randomly.
Out of the frying pan - S6-E16
Continuity mistake: At the park, Charlotte grabs the dog with her left hand raised. Shot cuts and now it's her right arm raised instead.
Out of the frying pan - S6-E16
Continuity mistake: When Charlotte is running at Central Park she outruns a woman with a grey woolen hat and stripped jacket. Shot changes and Charlotte is meters behind her, then outruns her again.
Out of the frying pan - S6-E16
Continuity mistake: The first shot of Charlotte's frying eggs shows the lower egg close to the pan's edge. A shot later it's on the middle part of the pan.
Out of the frying pan - S6-E16
Continuity mistake: When the episode starts, Carrie's left hand is on Alek's coat collar or not, depending on the shot. This changes several times.
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