Well, I always assumed since the whole story is really a retrospective, (and that the books themselves were theoretically started by Bilbo then later edited by Frodo) that they first used the only known name for Gollum (they never mention Smeagol in the Hobbit). It was Gandalf who first mentions Gollum’s real name is Smeagol, while they are in the mines of Moria (in the movie). For the most part, excepting the Elves and Frodo, everyone calls Smeagol by the name of Gollum.
Not to be a dork about it, but the Citizen Kane thing isn’t a continuity error anyway. It’s a plot hole, if anything. Let’s keep it on topic, people! 
I assumed the prologue was an “omniscient-narrator” type, since it began with a black screen with only singing in the background,
(silmarillion spoiler)
symbolic of the way the universe started.
But later it seems that it is voiced by Galadriel, and Galadriels monologue in TTT (seemingly out of place) makes it seem to me that the ROTK may END with a monologue by her as well. So perhaps the narrator IS Galadriel?
I understand why they did it (so as not to confuse audiences.) I just expected better from an omniscient (“for none now live who remember”) narrator.
In addition, John Mahoney, the actor who plays Frasier’s dad, appeared on an episode of cheers as a completely different person, Sy Flembeck. In that link you have to scroll down to the “Notable TV Guest Appearances” section.
I can’t believe nobody has this one yet…and Pulp Fiction has already come up.
When Jules and Vincent kill Brett there are already bullet holes in the wall behind them…yet the guy hasn’t come out of the bathroom and unloaded his hand cannon on them, which causes the bullet holes in the wall (but not Jules or Vincent). The fact that Jules has no holes in him is the basis for a complete scene later (or I guess it is also the reason Jules has ANY more scenes, just sayin’)
I haven’t seen it in a while, but some friends & I picked up this same continuity flaw while watching it on video many years ago. IIRC, the imminent takeover of the Earth by Terminators was stated as taking place in 1995, and there are a few reference to it being “three years away.” That definitely means the film takes place some time in 1992. During Sarah Conner’s hearing with the police, they definitely remark that she was involved in a shootout at a police station in 1984. So, there is only an eight year gap between the films.
Actually, Edward Furlong’s age isn’t nearly as ludicrous as the idea that a 13 year old peddling a ten speed bike can outpace an 18-wheeler rig (with the peddle to the meddle) that is pursuing it.
This was mentioned on the “Frasier” episode when Sam came to visit Seattle. Sam reveals to Martin that Frasier claimed his father was a psychiatrist and was dead. Frasier admits he’d said that because he was angry at him. When Niles asked what Frasier told the Cheers gang about him, Sam says he “never, ever mentioned you.”
As far as Star Trek dis-continuity, my biggest gripe is Data’s cat Spot. For several seasons, Spot the cat is referred to as a “he.” Then, in the godawful “Metamorphosis” episode, Spot is female, is pregnant, and delivers a litter of kitties! WTF???
And for the record: “The Simpsons.” OK, I know the creative people deliberately throw in inconsistencies from time to time just to piss off nitpicky fans. So there’s no use pointing out inaccuracies. But what does bug me is the way that baby Maggie simply disappears whenever it is inconvenient to have her around. The “spring break in Florida” episode is a good example. The family is arrested, forced to serve as servants, and then goes on the lam. Maggie simply doesn’t exist in this episode!
Popeye has the same problem.
When the cuffs fell off of her; she was said to be a “Teeny Houdini”.
It was a dirt bike (still doesn’t make it any less ludicrous) and Judgement Day is always mentioned as August 29, 1997. OK, I forgot about the three year thing but that still only pushes us back to 1994.
Not only that, but one of the cars downshifts more than forty times in the course of the chase. That’s a lot of gears.
Also, in Pulp Fiction: when Butch and Marcellus are in the dungeon, Butch has an enourmous sweat/blood stain on his shirt. He escapes and goes upstairs, and the stain is much smaller. He grabs a sword, goes back downstairs, and the stain is huge again.
Raise you a ‘Rape of the Vampire’ in which the entire cast is killed off half way through the film, and then reappear (and not as vampires, just reappear as they were). Though in Jean Rollins’ defense, the film was adapted to full length from a short he had made earlier.
The entire time continuity of ** O Brother Where Art Thou** is screwed up. The whole thing is supposed to take place within a handful of days (the pressure on George Clooney to interfere before his wife remarries). Yet in that time they produce a record, print it, and it hits the distribution channel so hard that copies are sold out and selling like wildfire. This is with 1930’s deep south distributions
Another point, Clooney is talking with a store keeper about a needed part for their car and the storekeeprer tells him it will be 2 weeks to get teh part. In their next scene, the car is seen running properly again, guess the part weren’t so critical.
I’m surprised no one has brought up the amazing colossal continuity issues in the Evil Dead films (other than the smaller “one sword becomes two” error mentioned earlier). Ash is killed (apparently) in the first movie, and returns alive in the second, which proceeds as if the first one never happened. Now contrast the ending of Evil Dead 2 with the beginning of its sequel, Army of Darkness. In part 2, Ash arrives in the Dark Ages to be worshipped as a god because he killed a Deadite. In Army, he doesn’t kill anything and is immediately taken prisoner. That’s only the beginning of the differences.
To be fair, though, I don’t think you can call these “errors,” because from everything I’ve read about the films, Sam Raimi knew they were a continuity nightmare and just didn’t care. That Sammy, he is so crazy! 
That wasn’t their car. As they leave the store, another car pulls up and a guy gets out to go into the store. Clooney and his compatriots promptly steal this car and use it for the remainder of the movie.
Actually, they do state the date for T2 - well, sort of.
When the T-1000 looks up John on the computer in the police car it lists his age and date of birth. ICBW, but IIRC he’s ten years old and was born on 28th February 1985. This is inconsistent with William Wisher’s novelisation of the original book, which had John conceived in early March, but forgiveable as it’s a very minor detail that didn’t make the first movie.
Also, when the T-800 gives Sarah Connor the history of Skynet it informs her that the microprocessor Dyson is working on is perfected three years after the present date; allowing a few months for Skynet to be funded and built after that, that would make it some time early in 1994.
So there’s a year dropped out somewhere, but it’s not as cataclysmic as some have made out.
Commando: The Yellow Porsche that the guy from Warriors is driving changes from a late 60’s model with a small spoiler to a mid-70’s model with an enormous whale tale several times during the chase. Then Arnold rams it so that it tips over on its side. A few moments later they tip it back over, get in, start it up and drive it away…without a scratch on it.
Starship Troopers: (I just saw this one, so it’s fresh in my mind). Denise Richards has been stabbed through the shoulder by one of the bugs, but a few minutes later gets up and starts firing a machine gun as they escape. As someone who recently had a Grade II shoulder separation, I can confidently state that she would have spent that escape scene screaming in agony, dragging her useless arm behind her.
Don’t forget the windows on the 18-wheeler which can clearly be seen shattering when the thing drives off the overpass, only to magickally reappear in later scenes.
In Jurassic Park, when they find themselves pitched into a T. Rex cage and there’s suddenly a cliff where there wasn’t one just a few moments before.
Don’t forget Sean Connery’s magic collar in The Untouchables
Well, it is somewhat tricky to tell what gender a cat is. Maybe no one ever bothered to look?
Not unless in the 24th Century they neuter toms by cutting their nuts off entirely, instead of just vasectomising them as they do today.