The One with the Dozen Lasagnas - S1-E12
Revealing mistake: After Phoebe tells Rachel that Paolo made a pass at her, we see a shot of the outside of Monica's apartment block and Rachel is throwing Paolo's clothes out of the window. Look closely and you can see the clothes have been very badly superimposed on to the background. (00:17:05)
Suggested correction: The show sent a crew to New York to film the clothes being thrown from the same building that is used in establishing shots. In a wide-screen version of the episode, the clothes can be seen being thrown out a window (although in the episode the clothes are supposedly thrown off a balcony).
The One with the Dozen Lasagnas - S1-E12
Revealing mistake: When Rachel throws Paulo's clothes over the balcony, they land on the corner of the building, yet the balcony isn't near the corner as there are bedrooms between the place where she throws them and the edge of the building. (00:17:15)