Factual error: This mistake is from series 6 onwards, with Ross' new apartment: There is an impossibility with Ross' kitchen, but not all of the time. It depends on the layout of the hallway outside his apartment. If the hallway continues along for a bit before going left or right, then the kitchen should stick out. However, when the hallway is a dead end, the kitchen fits ok.
Factual error: The makeup on Rachel's face "can't be covered up with makeup," and "won't come off," we learn in The One In Vegas, Part 2. So it's not a surprise that she still wakes up with it on (and so does Ross.) but an hour or so later, when she's at breakfast, it's not there. An hour or two won't make the magical difference that 8+ hours didn't.
The One With Joey's Porsche - S6-E5
Factual error: Phoebe discovers that one of the babies has wandered away, and finds the baby inside the open drawer. Yeah, no. These babies aren't even walking yet, much less are they able to lift themselves up past the height of their own bodies and launch themselves into a drawer.
The One Where Ross Got High - S6-E9
Factual error: A really picky one: When Ross looks at the recipe book, he says Rachel's made 'half a Shepherd's Pie'. Technically, a Shepherd's Pie is made with lamb, whilst it's a Cottage Pie that's made with beef (although the two names are often interchanged).
The One With The Proposal, part 1 - S6-E24
Factual error: There's no charity event in the world that would be clamoring for non-paying guests and offering them free food and an open bar.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.