The One With Monica's Thunder - S7-E1
Visible crew/equipment: After Ross walks in with the champagne and candy bar, in the shot of Monica shouting, "I'm getting married...," on the balcony, studio lighting can be seen inside above Joey.
The One With The Proposal, part 2 - S6-E25
Visible crew/equipment: After Joey fibs and tells Chandler that Monica went to her parents, when Chandler and Joey walk into the apartment, in the shot facing the hallway we can see some of the camera equipment past the doorway, and in the next wideshot of the apartment as the camera pans to Monica the overhead studio lighting rigs can be seen at the top of the screen.

The One With The Apothecary Table - S6-E11
Visible crew/equipment: When Phoebe and Rachel stop in front of the Pottery Barn window, in the first shot facing them from inside the store window the end of the brick set wall can be seen, with the camera beside it, and can also be seen when Phoebe comments that it's their exact living room.
Visible crew/equipment: When Ross notices that Ugly Naked Guy is back, in the next exterior shot we can see the top of the set as everyone gathers at the window.

The One In Barbados, part 2 - S9-E24
Visible crew/equipment: While Joey's wearing the snorkel gear he blows a grape out of his snorkel tube, and when Charlie walks into the room the opening in the wall can be seen beside the door.

The One With The Mugging - S9-E15
Visible crew/equipment: When Ross walks into Central Perk and Phoebe asks him about his class before she tells him the truth, in the closeup of Ross the camera can be seen at the right side of the screen.

The One With Rachel's Other Sister - S9-E8
Visible crew/equipment: When Monica heads to Joey's apartment to get the pies Joey tells her it's just one pie now, and after Monica's comment about losing the will to scold we can see the hole in the wall beside the front door.

The One With Rachel's Other Sister - S9-E8
Visible crew/equipment: When Monica tells Joey that he has a red plate instead of a fancy plate because it's a game, just as Joey says that he can't believe he won, we can see the camera at the right side of the screen.

The One With Ross's Inappropriate Song - S9-E7
Visible crew/equipment: While Chandler and Joey are watching Richard's videotape, when Chandler's relieved it's just football he heads off to get beer, and in the next shot as he hears the sound of moaning we can see the opening in the wall behind the TV.
The One Where Chandler Takes a Bath - S8-E13
Other mistake: In the opening scene, while Joey's eating the bowl of Frosted Flakes the box is on the counter, and the brand name "Kellogg's" has been painted blue with its white line extended and covered with a sticker. At the end of the episode, when Joey's eating the Cocoa Puffs the box on the counter has the brand logos for General Mills covered with stickers on the front and sides.

The One Where the Monkey Gets Away - S1-E19
Continuity mistake: While Rachel's babysitting Marcel she's watching the soap opera on TV, and when she points out Dr. Francis there's a closeup of the TV and when she points out Raven there's another closeup, but the TVs in both closeups are different, as well as the items that are near the TVs.

The One with All the Poker - S1-E18
Continuity mistake: When Chandler and Ross are explaining how Joey cried during their poker game, Joey's coffee mug is blue when he's holding it at the counter, but when Joey walks away from the counter his mug is yellow.

The One With All The Resolutions - S5-E11
Visible crew/equipment: After his fiasco with the leather pants, powder, and lotion, when Ross is at Monica's and tells the others he's going to kiss Ben goodnight, as he starts walking to the bedroom the camera can be seen at the right side of the screen.

The One With Ross's Sandwich - S5-E9
Continuity mistake: After Joey makes up the story about how he slept with Monica once in London, in the shots facing Phoebe, Rachel, and Ross the door to Monica's apartment goes back and forth being either wide open or closed, depending on the angle of the shot.

The One With Ross's Inappropriate Song - S9-E7
Visible crew/equipment: When Joey jumps on Chandler to shield him from seeing Monica's sex tape, the mat they land on is visible prior to the scene.
The One Where Chandler Doesn't Like Dogs - S7-E8
Continuity mistake: In this episode, it is stated that Ross does not like ice cream because it's too cold. However, back in The One Where Ross Dates a Student, you can see Ross on a date with Elizabeth eating an ice cream.

The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Ross, Chandler and Joey are setting up Ross' furniture and Ross is bent down saying, "And I cannot feel my legs," Ross is holding up a manual. When it cuts, the manual is suddenly lying on the floor. [In other versions, such as Netflix, the first shot shows the manual falling to the floor and the second shot does not exist. However, the mistake is valid for the TV broadcast version of the episode]. (00:11:45)
The One with the Dozen Lasagnas - S1-E12
Plot hole: At the end, Phoebe and Monica are sitting at the table eating the meat lasagna. Phoebe would not eat this as she is a vegetarian. (00:21:35)
Suggested correction: Early on in the episode, Monica suggested vegetarians can scrape. It is possible that Phoebe is doing exactly that. Also, two episodes later ("The One with the Candy Hearts"), it is revealed that Phoebe, in fact, does enjoy meat, as long as no-one tells her it is meat she is eating. She is poor and has never been able to afford meat.
The One With All The Thanksgivings - S5-E8
Continuity mistake: In the flashback where Joey sticks the turkey on his head, the subtitle says Thanksgiving 1992. However, the show started in 1994 and Joey didn't move in until the previous fall, so the earliest Thanksgiving that he was there would have been 1993. (00:04:30)

The One With The Cheap Wedding Dress - S7-E17
Continuity mistake: Monica chooses a wedding dress at an expensive boutique, then later goes to a discount store to buy the same style dress at a half-off sale. The dress she buys is different from the one in the boutique, having wider and frillier straps. When she tries it on later at the apartment, it is now the same style as the one at the boutique. (00:04:00 - 00:07:15)