Continuity mistake: Apparently Ross is Monica's older brother but in "The one where they're going to party", Joey states that the three men are all the same age ("we're 29, we're not women"), and in the one with the birth Monica says she is 26 and Joey says he is 25. If Joey is younger than Monica, and Ross and Joey are the same age, then there's definitely a mistake somewhere.
Continuity mistake: Across Series 3 - 5, Ross remains the same age (29) for all three years. In Series 3 he tells Chandler, "No thanks, I'm 29" when offered chocolate milk; in Series 4 when the guys try to party without Gandalf they all say they're 29; and in Series 5 when he's trying to reconcile with Emily, he says either he does, or he would get divorced for the second time before age 30.
Other mistake: In his apartment from later episodes, Ross' kitchen door is on the same wall as the front door, and it is a long and narrow kitchen, but Ross' apartment is between two others. The floor plan doesn't make sense unless the kitchen is only a foot wide, otherwise it would jut off into the hallway.
Continuity mistake: Ross always had an end apartment. Some point in Season 8, his apartment became a middle apartment. In earlier season, when Joey had mistaken Ross' for the hot girl's apartment, it showed the apt as an end apt. In TOW Joey tells Rachel, when Joey asked Rachel to have dinner at Ross' apt, it showed another hallway where Joey came from which is supposed to be the wall/ Ross' kitchen.
Other mistake: In 'The One With The Ick Factor' (Season One) Monica states that she is 26 years old. This episode takes place in 1994/95. However there are numerous other episodes such as 'The One With All The Thanksgivings' that show Monica and Rachel (who are the same age and in the same class) still being in High School in 1988. In 'The One Where The Stripper Cries' the two have to sneak into a college party in 1987 as they are still high school age. They should be at least 19 or 20 in 1987/88.
Factual error: Phoebe's greatest love David leaves her to go to Minsk and comes and goes throughout the whole show, telling stories of Minsk on the way i.e. of the long months when the sun does not rise and the constant freezing cold. Minsk, being the capital of Belarus (although claimed to be in Russia for reasons explained in Corrections), is approximately as high up north as i.e. Wales and northern coast of Germany, and even during the winter months there is always daylight for several hours. Although winters in Eastern Europe are cold, the kind of coldness described by David would more believably happen in Siberia than Minsk, and the summers are just as nice and hot as everywhere in Europe.
Other mistake: In almost every season when the friends are in the coffee shop, it shows a front view of Central Perk; and a lot of times, in different episodes, the same (unaging) lady with blonde curly hair is walking past the shop. There are also a couple of different episodes where two babies with red hair are being carried past the coffee shop.