The One With Ross' New Girlfriend - S2-E1
Other mistake: After Rachel takes the phone from Ross and hangs up on Julie, when she's sitting at the table there's a bottle of Evian water in front of Monica with part of its brand name covered - the letters "e" and "n" are whited out leaving "via" on the bottle.
The One With The Bullies - S2-E21
Continuity mistake: When the bullies are about to fight with Chandler and Ross, they decide to put all watches and keys into a hat. He takes the hat off and places it down and everyone puts the watches and keys in. The shot changes to a further out view and the bully has a different hat on his head while another hat is still placed where he put it. When there is a closer view of him, there is once again no hat on his head. (00:19:30)
The One Where Joey Moves Out - S2-E16
Other mistake: When Rachel is showing Phoebe her heart tattoo, the tattoo isn't dressed and covered, nor is the skin around it red or swollen, despite the fact she just finished getting it. (00:14:09)
The One With Ross' New Girlfriend - S2-E1
Continuity mistake: When Chandler has just got back from seeing Joey's 'bad' tailor, Joey says, "That's how they do pants". Chandler turns to look at him twice. (00:17:30)
The One Where Old Yeller Dies - S2-E20
Continuity mistake: A woman and a man in a blue shirt exit the coffee shop twice.
The One With The Bullies - S2-E21
Continuity mistake: A woman and a man in a blue shirt exit the coffee shop twice.
The One With The Bullies - S2-E21
Visible crew/equipment: While driving the cab, Phoebe is wearing a blue shirt. When the car stops suddenly, a crew member wearing a white shirt is visible driving the car.
The One With Ross' New Girlfriend - S2-E1
Revealing mistake: At the end, when Rachel and Ross are talking on Monica and Rachel's balcony, the edge of the "brick" wall behind them has a gap in it. The facade is obviously a thin plastic sheet made to look like bricks and mortar, and it has pulled away from the surface it is attached to.
The One Where Old Yeller Dies - S2-E20
Continuity mistake: When Monica asks Chandler and Joey to take Richard to the Knicks, Joey tells Monica, "We will bring him, but only if he takes the Jaguar." Chandler then drops his head in mortification, and the scene then cuts to focus on Monica's expression. In the right corner of this cut, you can see Chandler is looking ahead, and his mouth is moving saying "what am I supposed to say", but there is nothing being said during this scene. The camera then cuts to a different angle where Chandler lifts his head from the earlier drop just before he speaks to Joey. (00:04:30)
The One After the Superbowl, part 1 - S2-E12
Audio problem: When Phoebe is showing the children her guitar in the library, her voice comes on saying, "I know," when the children are amazed by her guitar. Look carefully - her lips are not moving when she says this.
The One With the Baby on the Bus - S2-E6
Continuity mistake: When Chandler and Joey fetch Ben from the Department of Health Services, as they say they're both the baby's father, Chandler puts his arm around Joey and Joey takes his hand. When the angle changes you can see Joey's shoulder and Chandler's hand isn't on there. When it cuts back to the front view, his arm is around Joey again. (00:15:10)
The One With Barry & Mindy's Wedding - S2-E24
Continuity mistake: Phoebe takes out her gum before kissing Joey. After she kisses him, she makes a comment about it and her mouth is empty. In the next shot, she sits down and is chewing. But she doesn't put the gum back in. (00:02:22)
The One After the Superbowl, part 2 - S2-E13
Visible crew/equipment: When Joey walks into the bathroom and starts whistling, the shadows of the camera and a passing crew member can be seen on the door of Chandler's cubicle, then the camera's shadow moves as Joey walks toward Chandler and also when Joey's about to stand on the toilet.
The One With the Breast Milk - S2-E2
Continuity mistake: When Phoebe tests then tastes the breast milk, Ross is holding Ben. Every time the camera goes back to Ross, the baby has his dummy in, then out, then in again, but no sight of Ross putting it in his mouth.
The One Where Heckles Dies - S2-E3
Continuity mistake: After she breaks Rachel's seashell lamp, Monica puts her jacket over the back of the big chair. When Chandler sits on it, the jacket keeps disappearing and reappearing in almost every shot. (00:17:35)
The One Where Heckles Dies - S2-E3
Continuity mistake: When the gang and Mr Treeger watch the paramedics take Mr Heckles away, a thin dark object like a camera mark or a pencil suddenly appears on the floor close to Ross' feet. (00:03:25)
The One Where Ross and Rachel...You Know - S2-E15
Visible crew/equipment: While Ross is trying to fix the position of the cavemen in the museum, a boom mic can be seen above his head.
The One With Two Parties - S2-E22
Other mistake: When Ross is at Monica's party getting Mr. Green's glasses and cigarettes he bumps into Mrs. Green and ends up having to come up with an alibi for the glasses and cigarettes. He then puts the glasses on, puts a cigarette in his mouth and says 'In fact I'm gonna go out into the hallway and fire up this bad boy'. At this point he walks past Rachel but he stops still as if frozen mid-step just before the shot cuts to him walking out into the hallway.
The One Where Eddie Moves In - S2-E17
Continuity mistake: In the previous episode, Joey tells Chandler that the bathroom in his new apartment has mirrors on both sides of the toilet. But in this episode, when we see the toilet from the side while Joey gives the gang a tour, it is clear that the wall is devoid of mirrors.
The One Where Ross and Rachel...You Know - S2-E15
Visible crew/equipment: When Rachel's talking about when Richard kissed her when she was a little girl, you can see the boom mic above her head. (00:16:10)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.