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.
Revealing mistake: When Monica leaves the apartment and Chandler stays listening to the answering machine, check the wall beside the door. It changes the angle, as if somebody moved it (probably to hide the hall).
Continuity mistake: Chandler and Monica are having dinner with her parents. He asks Jack how he and Judy got engaged. He starts, "Well I'd gotten Judy pregnant..." In an earlier episode they talk about how Jack told Monica's friends a "scary story" about how Judy got pregnant because her method of birth control, her diaphragm, had malfunctioned (damaged by a dog). In the rest of the show, however, we are continually hearing that the firstborn, Ross, was "a medical marvel" and that they thought Judy was barren. This apparently is the main reason why they love Ross more than Monica.
Factual error: Before Ross goes out to play the second half of the rugby game, Emily gives him some tips on how to hurt the other guys. She singles out one of the guys, saying he doesn't wear a cup. These guys are all English players who love rugby. Rugby players would NEVER wear a cup for rugby is more of a grinding sport than hit and miss. These guys would be crazy to wear a cup.
Continuity mistake: The beginning to series 7 takes place right after series 6 ended, basically Chandler has only just proposed to Monica. Yet Monica's hair is visibly different; at the end of series 6 she had no fringe and a center parting, now she has a fringe. Also Chandler, is visibly thinner, with a gaunt face due to losing 20 lbs in between the two series. Rachel also has had a hair cut, her long extensions have been removed and she is back to her usual hair length.
Revealing mistake: During the end bit, before we get to see Phoebe when she is being interviewed at Lara and Jeni's Massage, if you look closely at the name of the massage parlor, you'll see that, although the camera shakes and bumps, the words stay on the very same spot on the screen. Obviously the canopy was blank and the name was digitally added later.
Continuity mistake: When Rachel suggests to Joshua that they should get married, he says "What?", and his hands are out in front of him. The camera cuts to a wide shot and his hands are now on his thighs. Cut back to Joshua and his hands are now out in front of him with his fingers interlocked.