The One with the Sonogram at the End - S1-E2
Factual error: The sonogram shows a fetus that's much too far-developed for Carol's pregnancy. That fetus is at least 20 weeks along. (00:22:00)
The One with the Fake Monica - S1-E21
Factual error: The monkey is allowed outside his cage at an airport gate. Animals, with the exception of assistance dogs, cannot be transported in the cabin with passengers, and this rule applied in the 1990s as well. There is no way a monkey would be brought through a security checkpoint into a terminal concourse of a NYC airport and allowed aboard a regular commercial airliner.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.