The One With a Chick. And a Duck. - S3-E21
Revealing mistake: When Joey comes in with the shoebox containing the chick, it looks like a normal sized box, about 5 - 6 inches deep. But when Joey takes the lid off, we can see that the chick must be elevated on something inside the box, since we can see its entire body. Surely, the chick can't be more than 6 inches tall? (00:05:05)
The One With Phoebe's Ex-Partner - S3-E14
Visible crew/equipment: Just after Chandler says "I'm the smallest person in the world", and Joey comes out of his room, check the top left of the screen - you can see a boom mic track Matt LeBlanc across the set, and the bottom of some stage lights in the middle. (00:14:40)
Visible crew/equipment: When Bonnie first arrives at the beach house, when she enters the door look at the top of the screen above the left door and you will see a microphone dip into the shot for a second before the camera changes. (00:10:55)
The One With The Ultimate Fighting Champion - S3-E24
Continuity mistake: In the scene with Robin Williams and Billy Crystal, there is a shot of Rachel, and her hair is hanging straight down. The next shot of Rachel is from a different angle and there is a section of hair behind her ear; in the shot after that it is hanging straight again, and is then behind her ears again. (00:00:40)
The One With The Flashback - S3-E6
Continuity mistake: When Ross is talking to Phoebe and puts shot glasses on the bar, they're in groups. In the long shot, they're in a straight line then in a closer shot they're in groups again. (00:17:20)
The One Where Monica and Richard Are Just Friends - S3-E13
Continuity mistake: Monica and Richard are squishing tomatoes; when she starts dabbing his shirt with club soda the door behind them leading to Monica's room goes from open to shut between two shots. (00:08:30)
The One With The Giant Poking Device - S3-E8
Revealing mistake: The giant poking device is supposedly long enough to reach right across to the next building, but after they wake up Ugly Naked Guy, Joey says "retract the device!" and after pulling back about a foot of it the end suddenly pops up at the bottom of the screen. (00:20:25)
The One With The Tiny T-Shirt - S3-E19
Continuity mistake: When Joey and Kate are talking for the first time, Joey is holding a mug. Between shots, sometimes he is holding the mug by the handle and sometimes by the mug, with the handle sticking out. (00:04:40)
The One The Morning After - S3-E16
Continuity mistake: In previous episodes we've seen that from the living room there's a short wall just inside Monica's bedroom (presumably to prevent a clear view inside, as her bedroom set isn't normally there). However in this episode when most of the gang are in her room, they're listening right by the door into the living room with nothing in the way. (00:11:25)
Continuity mistake: Near the end, when Joey is asking Ross if Bonnie's room will be free tonight, he is pointing his hands at Ross. In the very next shot they are in his pockets. (00:20:50)
The One Where No One's Ready - S3-E2
Continuity mistake: The amount of fat in the glass differs throughout the length of the episode. (00:00:05 - 00:15:00)
Continuity mistake: When Phoebe goes to the other Phoebe's house, it's raining, but when Phoebe gets into the house her hair and her clothes are dry. (00:05:00)
The One With The Ultimate Fighting Champion - S3-E24
Visible crew/equipment: When the friends are leaving for dinner, and Phoebe stops Rachel to ask her about Bonnie, the stage lights are reflected in the TV. (00:06:00)
The One With Ross's Thing - S3-E23
Revealing mistake: When the car catches fire you can see that the fire is not in the car but behind the car. (00:05:00)
The One Where Monica and Richard Are Just Friends - S3-E13
Revealing mistake: When Richard gets tomato juice on his shirt and Monica goes to get some soda for it, you can't see any juice on his shirt. (00:08:25)
The One Without The Ski Trip - S3-E17
Continuity mistake: When Chandler tells Rachel to "shut up; you're not my mom," Joey has both hands on the bottom of the Chinese food carton. In the next shot his right hand is on top of the box. (00:05:30)
The One Where Ross And Rachel Take A Break - S3-E15
Continuity mistake: When Cloe hands Chandler and Joey the flier, it goes from flat to folded to flat in 2 camera cuts with no time to do it. (00:03:15)
The One Where Rachel Quits - S3-E10
Continuity mistake: At the start of the scene in which Ross breaks the little girl's leg, we can see that the stairs are just separated by railings. Later in that scene, when Ross and Chandler start walking up the stairs, there are walls on both sides of them. (00:01:40)
Suggested correction: This isn't completely true. In the first shot, we see railing in the middle, as shown in the screenshot. Then, the shot changes to upstairs, looking down, and we can see the wall, as shown in the bottom picture. However, at the end of the wall, it goes into the railings, which is visible just as the pair start to climb the stairs. A screenshot of this can be seen here: https://ibb.co/bmZ8xTc, making it easier to understand.
The problem with the screenshot is the right side is circled to show there's no railing, but the railing is on the left side (to the character's right), but Chandler is blocking the view of the railing. Ssiscool's screenshot is before Chandler starts to walk up the stairs, which is why it's seen.
The One Where Rachel Quits - S3-E10
Continuity mistake: The gang enters Monica's apartment and it is full of dead Christmas trees. After everybody has entered the apartment we see that the apartment door is shut; the shot then changes to the gang around the sofa, but in the next shot when Rachel answers the phone we can see behind her that the door is open. (00:19:00)
The One With The Hypnosis Tape - S3-E18
Continuity mistake: When Frank Jr is sitting in front of the TV while Davey and Goliath is on, his hand is along the edge of the TV set; however when Phoebe walks in, his arm is straight out. Then when Mrs Knight comes in, his head is straight down and the arm is back along the edge. (00:15:15)