Continuity mistake: After Will has arrived and Chandler says, "I'm watching the game but I'm not deaf," you can see Will in the background with his hands on his hips. When the camera switches to just Will and Monica, Will suddenly has two wine glasses in his hands.
Continuity mistake: Throughout the entire first scene where Rachel is asking Chandler and Monica if they have seen Joey and he's in the bathroom, Chandler is sitting at the table and his blue cup constantly switches from being in his hand to on the table much too quickly to be real movement. At one point he even holds a piece of food which then disappears from his hand back on to the plate.
Revealing mistake: When Monica and Phoebe are in Central Perk, Phoebe is looking through the list of ideas that Monica has come up with for the use of Phoebe's van. If you look closely (most obvious just after Phoebe says "let's plan the wedding reception") you can see that every single page of the notebook Phoebe is holding has the same thing written on it, instead of lots of different ideas that Monica is meant to have had.
Continuity mistake: Right before Ross and Rachel storm in, the girls show Joey how much their waxing stuff hurts. Phoebe starts putting the wax on Joey's inner arm, but then the shot changes and she is spreading in on the outer side. Also she slaps the strip on and the blue tab is hanging down off his arm, but then the shot changes again and it is on his arm with the other end of the strip hanging off the other side.
Continuity mistake: In the opening scene where Rachel is checking the mail and is walking over to Monica's room, she has a pair of pumps on, then once she has walked in on Monica and Monica runs after her to say she was taking a nap, Rachel is wearing a pair of backless high-heeled sandals, then when Joey and Ross come in, Rachel is wearing the pumps again (we see this when Ross says "I had to talk loud because the movie was loud").
Continuity mistake: When Monica and Phoebe are looking at the dollhouse, Monica says "I don't want a ghost for the house." When she says this, the camera is behind Phoebe whose right hand is up in the air. The shot then changes to Phoebe from the front, and her hand has instantly gone to her lap.