Continuity mistake: When Rachel is talking with Phoebe about Paolo,. she unrolls some kitchen paper and uses it as a tissue. Initially she's holding two torn halves attached to the roll, then when saying "He's a pig" it goes to a whole sheet not attached to any others, then when she sits down it's a whole sheet attached to the roll again. Plus when Phoebe sits too, in some shots the paper is on the table, in others it's not.
Visible crew/equipment: When Ross is on the balcony trying to comfort Rachel after she has split up with Paolo, we see a couple of shots from the balcony looking into Monica's apartment. If you look at the top of the screen you can see where the walls of the set end, and all the stage lights hanging from the ceiling of the studio.
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.
Continuity mistake: In the one where Ross finds out he's having a boy (series 1), just before Rachel lets it slip, she is sitting on the edge of a chair eating a cookie. Watch her dress, it changes back and forth from being undone from the waist up, to only having two buttons open at the top.
Continuity mistake: During the scene where Phoebe is telling Rachel that Paolo made a pass at her, Rachel unrolls a long length of kitchen roll. During the scene there is a shot over her shoulder where we see that the kitchen roll is as normal and in the next shot we see it unrolled again.