Continuity mistake: Carrie takes the fork to her mouth but a shot later her arm is lowered. (00:01:10)
Continuity mistake: Big reaches for his glass but a shot later it's already raised and close to his chest. (00:01:16)
Continuity mistake: When Charlotte bumps into her friend on the street, the passers-by are not continuous between shots. (00:23:55)
Continuity mistake: When Debbie talks about the Knicks she places her arm on Steve's back, but it disappears in the opposite shot.
Continuity mistake: When Big lies in bed and Carrie visits him, his right index finger is either lying on the green sheets or on his white robe, depending on the shot. This swaps back and forth.
Continuity mistake: The number and colour of the domino tiles on the floor are not continuous between shots.
Answer: After its initial run on HBO, SATC was syndicated for cable TV. Syndicated series are usually edited for nudity, language, running time, and have alternate filmed scenes, etc. Maybe you saw two different versions where an alternate narration was used.
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