An Older Than Print example: the original Beowulf gave no physical descriptions of Grendel or his mother, and as a result, their appearances often vary in adaptations. Grendel is usually portrayed as a brutal and ugly ogre, but sometimes he is a more-human (but just as brutal) barbarian warrior. His mother is often depicted as a hag, but sometimes as a Dark Action Girl, and modern depictions sometimes portray her as a demonic Shapeshifter who can assume the form of an attractive, seductive, human woman. (The original poem gave no real physical description of the dragon either, but let's be honest, a dragon is something that's pretty easy to picture.)
The Star Wars Expanded Universe has some very bad examples of this, especially in the long, interconnected series of novels. The New Jedi Order series (19 novels, 27 stories, 12 different writers) was legendary for this, and its followup, Legacy of the Force, managed to be almost as bad — despite being only three writers writing three books each.
Even before then, some parts of the Bantam Spectra-era Expanded Universe had some serious Character Derailment, depending on the writer. Largely this is because writers apparently didn't like one anothers' work and did as they pleased, ignoring the fact that the Star Wars EU is supposed to be continuous. This led to quite a few Fix Fics — and see that article for how this was eventually repaired in Canon.
In a word: Mando'a. Depending on the writer—that is, depending on whether the writer is Karen Traviss or not—the Mandalorians are either gruff, psychologically diverse mercenaries and warriors with questionable pasts and practicesnote like the fact that their race backed the Sith in every single one of the Sith/Jedi wars, or eternally morally-upstanding Warrior Poet heroes of Mary Suetopia who show the Jedi what they're really supposed to be like. Traviss' work has included A Jedi dropping his saber and joining them, and an attempt to justify Order 66. Traviss' moments of Small Name, Big Ego don't help matters.
Are Imperial stormtroopers a bunch of faceless mooks, poorly equipped, poorly armed, half blind, disorganized, blindly obedient, dim-witted, in fragile armor, easily killed, and fundamentally evil so it's okay to kill them? Or are they a widely disparate military force of individuals, who joined the stormtrooper corps for many reasons including the desire to protect civilians, who may question the orders they are given, who think of themselves as preservers of order and justice, highly trained and well equipped, a Badass Army that too often gets led by incompetents and evil people? Depends. Are you reading most EU novels, or are you reading anythingbyTimothyZahn?
Generally this depends on how much character development the Imperials get. For example, the TIE Fighter video game, which had the player as an Imperial pilot the entire time, have the Imperials on the right side of morality in virtually every battle, with some "questionable" secondary objectives.
Also any ex-Imperial military personal (Stormtrooper, Officer, Pilots, etc) instantly becomes elite if they join the Rebels or mercenaries. That is a pretty strong indication they are well-trained, just forced to use ridiculously bad tactics.
Another good one for a long while was Luke's love life. You could see the canon wars as practically every single writer made a new beautiful girl for Luke to fall for, convinced that his creation was the future Mrs. Skywalker. Timothy Zahn just got the last shot.
In his defense, Timothy Zahn also got the FIRST shot, in terms of the EU.
The Millennium Falcon's speed. Does "Fastest Ship In the Galaxy" apply to realspace and hyperspace both, or just hyperspace? The movies, Word of God, and several pieces point towards the former (the Falcon is clearly shown flying the fastest in Return of the Jedi, but some writers, perhaps drawing too much from the tabletop RPG, make it slower than fighters. But it was also shown being outrun by a Star Destroyer in "The Empire Strikes Back" (hence Han's line about "We can still outmaneuver them"), though admittedly this was while it was in a state of disrepair.
To a lesser degree compared to the worst examples, there's Vader and his You Have Failed Me tendencies. Sometimes we find out that guys like Ozzel were incompetent to the level that the Empire was truly better off without them. Other depictions have him as so choke-happy that officers draw lots to see who must report to Vader because even if you're bringing him news as ordered, he might kill you just because he's in the mood to do so.
Another Vader-related question is the matter of his lightsaber skills. Depending on who was writing Vader at any given time his swordsmanship could be anything from clunky but effective to unstoppable juggernaut to elegant fencer. Not helped by the disparity in Vader's film appearances (contrast especially his slow, jerky movements during his fight against Obi-Wan in A New Hope to his fast, twirling, casually masterful technique from Rogue One).
Pretty inexcusable overall is every writer meddling with the H.P. Lovecraft mythos.
H.P. Lovecraft never really attempted to portray his stories as a single, consistent mythos. A few names and ideas are shared, but there's no actual continuity. He was attempting to give the feel of a hidden mythology, and mythologies have no canon, being instead self-contradictory and inconsistent. One of Lovecraft's goal with his Mythos stories was the show a back story in which Depending on the Author was the dominant factor.
Which is rather fitting given the themes...
The problem is not the continuity, but the mood of the setting. For Lovecraft, it was heavily about how the universe just doesn't care about mankind. Later writers making humans more important and worth the notice of monsters is what is often complained about.
The War of the Spider Queen series of Forgotten Realms novels suffers from this trope very badly. In a sextology where each book was written by a different author, this sounds like it should have been inevitable, but RA Salvatorewas billed rather prominently as the series' editor (most likely for otherreasons). All of the characters got hosed with this from book to book, but Deadpan Snarker and fan favorite Pharaun Mizzrym in particular suffered from wildly inconsistent characterization in the later books of the series. And then was killed off.
There was also Halisstra, resident Heel Face Turner and Defector from Decadence, who was pretty consistent in her first few appearances as a scheming but not-particularly-cruel drow who jumped ship when a nicer deity than Lolth came down the line. Then after her conversion she got flanderized into an idiot who shouldn't have lasted a day in drow society and made some utterly boneheaded moves that ultimately got her forcibly converted into Lolth's Brainwashed and CrazyThe Dragon. Sigh.
The Eighth Doctor was played on-screen by a man who is about 5'8", and it happened to come up that he's 160 lbs fully (over)dressed with shoes on. He's no Noodle Person. He is shorter than average, with a compact, athletic build. Nonetheless, in the novels, even the same author sometimes cannot decide whether he is very tall and skinny, slight, or merely a little shorter than your typical human, Human Alien, or Ambiguous Human. Fitz, previously described as so tall he feels mismatched standing next to a woman who does not seem to be excessively petite, is in one scene surprised that a 6'6" young woman is taller than the Doctor. Who, like I said, ought to be a full ten inches shorter than her. This also happens to eye colour — in Fitz's intro book, his eyes are twice mentioned as gray, and once as blue. They eventually settle on gray. The Doctor's eyes can't decide whether to be pale blue, electric blue, blue-gray, blue-green, or green.
Also, almost every character is written inconsistently to some extent: Sometimes the Doctor is basically just an All-Loving Hero with a side of Cloud Cuckoolander, and sometimes everyone spends the whole book shouting, "What the Hell, Hero??!" at him. Fitz's intelligence fluctuates, and he runs the gamut of Kavorka Man, Chivalrous Pervert, and, on rare occasion, comes across as Doctorsexual. He once committed contempt of court because someone insulted Anji for her ethnicity, but he once asked her if her people speak Hindu, and continues bugging her even when she gets obviously annoyed — considering the fact his father was a German immigrant (hey, Fitz do your people speak Dutch or something?) and Fitz is most of the time practically The Chick in that once you get beyond the snark, he's a ridiculously sweet, caring person, it's all the more egregious. Then there's Sam Jones, who at first was a 'generic companion' with a wildly different personality in every story. The book Alien Bodies attempted to do a Fix Fic on this by saying she was created as a 'perfect companion' for the Doctor, fulfilling whatever role she has to.
Faction Paradox. Lawrence Miles created them as the Chaotic Neutral counterpart to the Lawful Neutral Time Lords. Pretty much everyone else wrote them as Chaotic Evil, to the extent that Miles basically disassociated himself entirely from what the EDAs had done with his ideas.
How do other characters see the Fourth Doctor's smile - dazzling and wonderful, rogueish and sly, or Nightmare Fuel? It's fair to say it's dependent on what the author themselves got from the performance more than anything. The short story Only Connect also describes his eyes as being 'soulful brown', peculiar since Tom Baker was well known for his strikingly blue eyes. (He was also drawn with brown eyes on the cover of the novelisation of "The Deadly Assassin", inexplicably as the artwork was obviously traced from a photograph).
This happens in the Dragonlance series of novels as well. Elves in particular can get very different portrayals depending on the writer. They are sometimes depicted as being vegetarians, and being disgusted with eating meat, or they are depicted as having no problem with eating meat. They are also sometimes depicted as having a somewhat different mindset than humans due to their long lives, other times they are very human-like and have no trouble relating to humans. The world as a whole can either be depicted as a gritty, medieval one, or a fairly tame Renaissance Faire-like world.
The Arthurian mythos. Dozens of medieval authors created works related to the Matter of Britain - and the number of knights, the location of Arthur's court, and countless minute details, tended to vary from one writer to another.
Atlanta Nights manages to do this within a single book, which makes sense considering that it's a collaborative hoax by several writers.
In the Hardy Boys spinoff series, The Hardy Boys Casefiles, the opening chapter of the first book Dead on Target has Joe's girlfriend Iola killed by a terrorist car bomb. Since the series was written by a great many ghostwriters, many ignored this fact for the most part, and Joe would slingshot between essentially a non-married grieving widower to his more typical fun-loving, girl-crazy self.
Land of Oz: Oscar Diggs, the titular Wizard of Oz, is very much a case of this, ranging from well-intentioned con artist with benign intent (Oz: The Great and Powerful), to a shady trickster who blundered his way into power through fortunate timing and technological prowess, to a malevolent Magnificent Bastard who uses existing conflicts within Ozian society to keep factions fighting each other while he maintains a singular pursuit of ultimate power (Literature/Wicked).