The One With The Proposal, part 1 - S6-E24
Other mistake: Joey bids on a Catalina 22 yacht, but the picture, and the yacht he and Rachel are on at the end, is a Catalina 18.
Revivi
The One With The Apothecary Table - S6-E11
Visible crew/equipment: After Ross and Rachel cover the table with the sheet, when Phoebe walks in Rachel says they can turn out the lights and watch the movie, and in the next shot we can see the end of the set wall, the soundstage and a crewmember's leg.
Super Grover

The One With Ross's Teeth - S6-E8
Visible crew/equipment: When Joey's in the kitchen holding a football waiting for Janine to come home, so he can talk to her about getting rid of the girly stuff, just as Janine walks into the apartment the camera can be seen at the right side of the screen.
Super Grover

The One Where Ross Dates a Student - S6-E18
Visible crew/equipment: While Phoebe and Rachel are with Monica in the guestroom, Phoebe decides that Rachel should be the one to get the nice room, and right before Monica tells Rachel that she's the first guest at "Hotel Monica" we can see the end of the bedroom set wall, with the kitchen and living room visible.
Super Grover

The One With The Apothecary Table - S6-E11
Visible crew/equipment: After Janine tells Joey that she'll apologize to Monica, in the shot of Janine walking into the hallway the end of the hall's set wall can be seen at the left side of the screen, and the corner of the camera can be seen moving at the right side of the screen.
Super Grover

The One Where Phoebe Runs - S6-E7
Visible crew/equipment: When Phoebe bends over to tie her shoelace before the first run, and later when she surprises Rachel at the park while running, the mic pack bulge under Phoebe's top can be seen on her back, and when Rachel bends over there's a bulge at her back as well. It's also a bit noticeable the third time they run.
Super Grover

The One With Joey's Fridge - S6-E19
Visible crew/equipment: When Professor "Frei.sen.stin.linder" walks in on Ross with Elizabeth, it then cuts to Ross, Chandler, and Joey walking into Joey's apartment, and we can see the opening in the wall where the bulletin board usually hangs.
Super Grover
The One With The Ring - S6-E23
Visible crew/equipment: In the opening shot of Phoebe and Chandler in the "nine millionth" jewelry store looking for a ring, at the top of the screen we can see the tip of the boom mic moving in the wideshot. Then just as Chandler looks into the display case and says, "Ugly ring. Ugly ring. Ugly ring," the boom microphone can be seen moving around in the mirror's reflection behind him.
Super Grover
The One With The Routine - S6-E10
Audio problem: When Ross has finished telling everyone the story of the dreidel, we cut to Monica and Chandler's reaction shot which shows Ross' mouth moving even though he is not talking. (00:01:30)
endubbThe One With Joey's Porsche - S6-E5
Revealing mistake: The triplets are supposed to be two girls and a boy; however, certain revealing shots of their anatomy when they are in Monica's apartment show that the two babies playing the girls are actually boys.
LeighaThe One With The Joke - S6-E12
Visible crew/equipment: When Joey announces that Central Perk will be closed for an hour he shows everyone to the door, and in the wideshot of people walking out the door we can see the camera turning at the top right side of the screen, just before the shot cuts away.
Super Grover

The One With The Routine - S6-E10
Visible crew/equipment: While Monica and Ross attempt to do the original end to their routine, instead of Monica catching Ross she jumps out of the way, and when Ross lands on the floor the corner of the crash mat can be seen. (Widescreen version).
Super Grover

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.
Super Grover

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.
Super Grover
The One With The Proposal, part 1 - S6-E24
Continuity mistake: In the scene where Richard is being seated next to Chandler and Monica, the amount of champagne in Chandler's glass changes. (00:09:20)
Pam-I-am
The One Where Ross Got High - S6-E9
Visible crew/equipment: After Ross and Monica blurt out each other's secrets to their parents, when Jack says, "And we kind of figured about the porch swing," in his closeup we can see the end of the set wall, with the soundstage behind it and many tape marks on the floor.
Super Grover

The One With Rachel's Sister - S6-E13
Visible crew/equipment: After Jill comes to Monica's apartment, they are all around the table in the living room. As the camera is moving from Jill, to Monica and Chandler, who are sitting on the couch, a camera-man is visible in the kitchen behind them, complete with camera and trailing wires. (00:04:15)
The One That Could Have Been, part 2 - S6-E16
Continuity mistake: Rachel is talking to Joey in his apartment after waking up the next morning, looking messy and rumpled. As she talks, her bra strap slips down her arm. In one shot (as she says "I'm a horrible person"), the strap is all the way down her arm and then in the next shot it is tucked under her shirt. (00:10:00)

The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: After Chandler has written the message on the Magna Doodle, the sliding eraser moves from the right to left side just as he leaves with Monica, and when Joey and Chandler are playing foosball, the barely legible "Joey" is now neatly written on the Magna Doodle, and its sliding eraser is again back to the right side.
Super Grover
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.
Super Grover
Answer: These are references to the TV show NYPD Blue. Deputy Andy Sipowicz is the name of one of the characters, whilst another character (Deputy Danny Sorenso) is played by Rick Schroder who previously starred in the show Silver Spoons.
pinkwafer