Other mistake: In the scene where Rachel is talking to Chandler in the hall, after she says "the 4th of July", it cuts to a shot from behind Rachel's head. If you look on the right hand side of the screen, you can see a piece of wood in the foreground. This probably came from Joey and Chandler's doorframe, through which this view would have been filmed. In addition, this door was supposed to have been closed throughout the entire duration of this scene.
Continuity mistake: In the scene where Phoebe tells the gang about her "Relaxitaxi" idea the position of Chandler's left arm changes between shots. In the frontal shots it's lying the back of the chair and in the shots from behind it's wrapped around Monica's shoulder.
Visible crew/equipment: When Chandler runs into the apartment to say Underdog has gotten away, a crew member can be seen reflected in the sun shaped mirror behind him walking through the back of shot. It can't have been Rachel, Monica, Phoebe or Joey because Joey is sitting down and Rachel, Monica and Phoebe are nowhere near the mirror.
Continuity mistake: When Rachel is talking to Joshua near the drinks table at the party, he is holding a blue cup in his left hand and nothing in his right (this is most obvious when she's offering him a cherry). When she begins to choke, he raises his empty right hand to pat her on the back, then when she walks away there is suddenly a bottle in his raised hand. The shot changes, and his hand is again empty and he reaches down to the table and picks up the same bottle.