Continuity mistake: When Rachel finds out that Ross and Julie are getting a cat, watch Rachel's tray. When she says "together?" she's got a towel that is flat; cut to Ross and Julie for a fraction of a second, then when it cuts back to Rachel saying "both of you?" it's now in a pyramid.
Other mistake: When Joey and Chandler and in the cab on the bridge, Joey quickly stops the cab so Chandler can get out. However, on the screen behind, the background doesn't 'slow down' as Joey does, it just continues as if the cab is going at the same speed. Then, in the next shot, it is still. When Joey sets off again, the background stays the same and doesn't show that the cab is getting faster.
Other mistake: When Chandler says "We just got married. Right there!" and points. We hear a small 'ding' and Monica asks "Is that your ring?" But when Chandler pointed, you can see that all of his fingers except his index finger are closed to his hand. So the ring couldn't have come off.
Continuity mistake: When Phoebe and Monica are at Monica's table and Phoebe is trying to convince Monica to go on a date with her date's translator, watch Phoebe's arm. She points at Monica when she says, "Don't call him that; his name is Spackleback Larry", but when the shot changes to a side view of them, she has her arm resting on the table with no time to put it down between shots.