Friends lasted for 236 episodes over 10 seasons, so it's not that surprising if it contradicted itself a few times over the years. It's full of small jokes that are inconsequential to the plot, so things might (and did) get mixed up.. BuzzFeed's Jen Abidor recently spotted one continuity error on Friends about Monica's feelings about arcade games, and it's so specific that it's a surprise no one caught it until now.
The episodes at hand are Season 6, Episode 3 "The One With Ross' Denial" and Season 8, Episode 12 "The One Where Joey Dates Rachel". In the Season 6 episode, Rachel is moving out of her and Monica's apartment, so Chandler can move in. Monica wants to make Rachel's old room into a "beautiful guest room" filled with antiques, flowers, and comment cards "so people can tell us how much they loved staying here." In response, Chandler suggests it be a game room with old arcade games. Monica very quickly dismisses that idea, and their storyline the rest of the episode is about how she can't deal with Chandler wanting to add his own style into the apartment.
It totally goes with Monica's personality that she would prefer a guest room to a game room — but wait! In Season 8, Episode 12, Phoebe surprises Monica and Chandler with a Ms. Pac-Man machine as a wedding present and Monica freaks out... in a good way. She says, "I practically spent my entire childhood at the arcade," and even suggests:
The rest of the episode is spent with Monica obsessively playing the game so she can wipe out Chandler's high scores where he made the initials say dirty words before Ross' seven-year-old son, Ben, comes over. By the next episode, the Ms. Pac-Man machine is gone.
So, what's going on here? Abidor puts forth, "Maybe it's a plot hole, or maybe Monica had repressed those arcade memories so much and only found them again once Ms. Pac-Man was in her apartment."
A BuzzFeed commenter, Alexandra Martin, wrote, "I'm going to chalk this up to Monica being against it at first because the moving-in together was still very fresh and she was having a hard time reliquishing [sic] control of *her* apartment. She also probably fully imagined how she would decorate the new guest room and an arcade game didn't fit her vision at the time."
Another commenter, copygift9980, thinks it had to do with Monica's love of gifts: "if anyone knows monica they know she loves gifts. Any present you give her she is hype about."
Another, Joshua Mims, wrote, "What if it wasn't a plot hole at all, but an insight into Monica's psyche." He continued, "Mrs. Pac Man is a woman who fights back by eating her problems. Monica is a hyper-competitive woman who spent her formative years being made to feel less valuable than her brother, who used food as a coping mechanism."
All interesting points — Especially that last one. Damn, dude — but this most likely was just a case of the writers doing what made the most sense for the characters at the time. It makes total sense that Monica would shoot down Chandler's game room idea. And, since their talk about arcade games wasn't a large part of that episode's plot, when it came time to do something about games that would be an entire storyline, they forgot about the game room convo. If that wasn't the case, the episode probably would've had Chandler say something like, "I thought you hated arcade games," at which point Monica could explain that she only loved Ms. Pac-Man and the vending machine, which she does say were her two favorite "games".
It should go without saying that this isn't that serious. Finding this inconsistencies in shows like Friends is part of the fun of re-watching them so many times. There could even be another mention of Monica loving — or hating — video games within the over 200 episodes. Someone in the middle of their 47th re-watch just has to spot it.