Continuity mistake: When Monica and Chandler walk into the apartment with the twins, 2 very bright yellow soothers keep appearing and disappearing from the babies' mouths. (00:18:50)
Revealing mistake: When Chandler and Monica try to change the babies, Courteney Cox's pregnant belly is visible. (00:16:20)
Continuity mistake: When Chandler and Monica are in the birthing room and they have just been told they are having twins, her scarf keeps changing from sitting on her shoulder to being over her shoulder. (00:10:20)
Continuity mistake: When Chandler and Monica are at the hospital holding the twins right before they try and swap babies, there are two hospital tags around Chandler's left wrist which then disappear before re-appearing. (00:15:25)
Continuity mistake: When Ross and Rachel are standing at Ross' door after Rachel comes over to say goodbye and they are hugging and talking, Ross' right hand changes from being on Rachel's shoulder to on her waist and then back to her shoulder. (00:00:35)
Continuity mistake: While Mama Joey is looking for Chick Jr. and Duck Jr., the things pinned to the bulletin board beside the door have vanished when Monica and Chandler walk in, but after Monica walks out to check on the twins everything's back up on the board like it was before.
Revealing mistake: When the first baby is born, Monica and Chandler are asked by the doctor if they would like to cut the umbilical cord. However, just before this line is delivered, the baby is moved and its navel is visible.
Continuity mistake: When Ross is talking to Phoebe and Joey in Central Perk, a strand of Phoebe's hair keeps getting snagged behind the buttons of her blouse and hanging loose again with her other hair several times during the scene. (00:12:40)
Continuity mistake: In the hospital when Erica is giving birth and the camera is on the doctor, the door to the room is closed. However, when the camera angle changes, the door is wide open even though no one had entered or exited.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.