The One Where They're Up All Night - S7-E12
Plot hole: It is made clear through dialogue in the episode that Joey and Ross are stuck on the roof because Joey removed the bit of piping holding the door open. However, when Tag, Rachel and Phoebe get up to leave, Phoebe says "Shh, get me out of here" and there is a clear shot of the door standing wide open. Afterward, it is possible to see Tag reaching for the door handle to close it behind him. This is inconsistent with the idea that the door needs to be held open. (00:02:20)
The One Where They All Turn Thirty - S7-E14
Plot hole: There's no way Phoebe has lived to 31 without knowing her birth date. She's had "real" jobs (like the massage parlor) and those require social security numbers and accurate birth dates. She didn't go to high school, but she mentions classmates, so she must have gone to elementary/middle school, and those required birth dates even in the '70s and '80s. She's also "lived in Prague," which she couldn't have visited without a passport - which requires a birth certificate.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.