At the party while Ross, Rachel and Phoebe are talking at around 16th minute, Ross is pouring a drink, in the next shot the bottle magically disappears and Ross puts his hands on his mouth.
You don't 'win' the Nobel Prize, you 'receive' it. There's a difference.
When the Bitter Woman on Stage starts yelling at Chandler, an extra sitting behind Chandler breaks character and start laughing.
During Joey's party, all the clocks on the buildings in the background don't move.
Just after Rachel hears the message from Jan Rogers she confronts Joey who explains he has to be up early and "work comes first". In the first angle, he is gesturing with his right arm, as the angle changes to Rachel, he is gesturing with his left.
When Ross and Charlie are sitting in the restaurant with Spafford the right side of Charlie's top is burst at the seems. This is particularly obvious during the line "When we exit, should we walk or run?"
During one of the stock NYC transition shots, you get a brief glimpse of the World Trade Center's twin towers, more than a year and a half after they were destroyed in the 9/11 attacks.
When Monica is talking with Chandler on the roof (around 21st minute) and she says "I got it when I was thirteen, very difficult", we hear the voice but Monica's lips don't move at the end of the sentence.