The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Monica is saying bye to Paul, Paul goes to the screen left but the stairs are at the screen right. (00:19:20)

The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: In the scene where the friends scoot the table over to see Monica's date with "Paul the wine guy", the cup in front of Chandler changes position. (00:18:55)
The One Where Dr. Ramoray Dies - S2-E18
Continuity mistake: When Monica is trying to cheer Joey up, she tells him that she straightened out his shower curtain so it wouldn't get mildew. But in a previous episode (The One Where Eddie Moves In), Joey gives the gang a tour of his new apartment; the shower is clearly visible in the bathroom, and it has a door. (00:18:10)
Deliberate mistake: The show is set in New York. Joey was a cast member on Days of Our Lives, which is filmed in Los Angeles, but is still always around.
The One With The Chicken Pox - S2-E23
Factual error: The symptoms (spots, fever, etc) of chicken pox only develop 2 - 3 weeks after exposure to the virus. Therefore, when Ross knew that Ben had chicken pox, Phoebe shouldn't have developed the condition until at least two weeks later, and Ryan certainly shouldn't have developed the disease until the end of his stay (as Phoebe was his only contact with the virus). (00:09:30)

The One With Joey's Porsche - S6-E5
Other mistake: Immediately after Joey walks in as Chandler is handling the baby, we see him staring and waving in a direction past the stage. (00:06:55)
The One with the Sonogram at the End - S1-E2
Factual error: The sonogram shows a fetus that's much too far-developed for Carol's pregnancy. That fetus is at least 20 weeks along. (00:22:00)

The One With Ross's Denial - S6-E3
Visible crew/equipment: After Ross tells Rachel about Warren's apartment he gives her Warren's phone number, and in the closeup while Rachel hugs Ross, and also in the following wideshots which face Ross the camera can be seen at the right side of the screen.

The One With Ross's Tan - S10-E3
Visible crew/equipment: After Monica gets the call from Chandler about the fake car accident and leaves Phoebe with Amanda, in the next shot of Joey walking into his apartment the bulletin board that usually hangs beside the door is cut to about a quarter of its size, and it's covering part of the hole in the wall.
Continuity mistake: Chandler and Monica's wedding day is May 15th 2001, as mentioned on the show. In Series 9, some time in January 2003 (as it is after the characters have celebrated Christmas and New Year), it is established that Rachel has been on maternity leave for five months, which means she took her leave in August. Since she realised she was pregnant in May the year before, when Monica and Chandler got married, this means her pregnancy lasted from April/May 2001 to August/September 2002, a time span of 16 to 17 months. This cannot be explained by saying that episodes don't have to take place in the month they air, as we are given the dates by the characters on the show.
The One With The Girl From Poughkeepsie - S4-E10
Factual error: Ross falls asleep on the train and ends up in Montreal, where the woman he meets tells him "it's only a 2-hour ferry ride to Nova Scotia." Yeah, more like a journey of between 13 hours (12-hour car ride plus 1-hour ferry) and 23 hours (multiple bus legs plus 1-hour ferry.) The character could have been lying to Ross, but it's not presented that way at all.
The One With Joey's Big Break - S5-E22
Factual error: Joey and Chandler are supposedly crossing the George Washington Bridge but the exterior background viewed from inside the car is very obviously a repeat reel of another bridge, and their conversation goes on for far too long for the actual crossing. And the cutaway shot after Chandler is kicked out of the car shows an aerial view of the Brooklyn Bridge.

The One With Monica and Chandler's Wedding, Part 2 - S7-E24
Revealing mistake: At the point in the ceremony where Joey forgets the rings, the camera pans out and you see Chandler step sidewards to get the ring from Ross, and Monica step sidewards to get the ring from Rachel and Phoebe. As Monica moves, her dress slides across and one of her feet is revealed; it has what looks like a brown boot or heavy brown shoe on it. (00:20:05)
The One With the Sharks - S9-E4
Continuity mistake: In "The One With the Sharks", Phoebe talks to Joey about how he's never been in a long term relationship. He has been, though - Angela Delveccio, who he went out with for three years. (00:21:40)
The One with the Blackout - S1-E7
Revealing mistake: When Chandler is choking on the gum, you can see it is still in the left side of his mouth in a huge lump. (00:16:45)
The One With The Prom Video - S2-E14
Continuity mistake: The prom video has just ended and the TV screen goes blank. Monica had been sitting next to Rachel, but in the reflection of the TV screen you can see her beginning to stand up. We cut back to a 'real' view, and she's sitting down; then she stands up again. (00:20:25)
Factual error: Phoebe's greatest love David leaves her to go to Minsk and comes and goes throughout the whole show, telling stories of Minsk on the way i.e. of the long months when the sun does not rise and the constant freezing cold. Minsk, being the capital of Belarus (although claimed to be in Russia for reasons explained in Corrections), is approximately as high up north as i.e. Wales and northern coast of Germany, and even during the winter months there is always daylight for several hours. Although winters in Eastern Europe are cold, the kind of coldness described by David would more believably happen in Siberia than Minsk, and the summers are just as nice and hot as everywhere in Europe.

The One With The Stain - S8-E7
Visible crew/equipment: When Brenda is cleaning the top of the cabinets, stage lights can be seen on the top right-hand corner of the screen. (00:11:45)

The One With All The Rugby - S4-E15
Continuity mistake: During the rugby game, when Ross tells Phoebe and Joey that he thinks he's dying there are two hairsticks in Phoebe's bun in the shots facing her, but there's only one hairstick in her bun in the shots facing Ross.

The One With Chandler In A Box - S4-E8
Visible crew/equipment: When Kathy walks in while Chandler's in the box, after Phoebe tells her, "He can't talk right now," in the shot facing Kathy the end of the set wall can be seen, and there's a plastic cup with a straw sitting on a shelf off stage.
Suggested correction: It's presented as sarcasm. Not a mistake.
Ssiscool
Not clear on where you got that it's presented as sarcasm; nothing in her delivery says so.