When I discuss my frothing rage for The Avengers with normal people, their first reaction usually has something to do with the fact that I'm a fan of, and read the comics. Most of the time this is a negative reaction, like, "Well, you liked the comics, of course you're going to hate the movie," and exactly once did somebody think that my embarrassing hobby might provide further insight into the movies. Both positions are wrong.
So let's talk about consistency. For the purposes of a lot of movies, especially the lower-brow, popular movies like superhero movies, movies based on fantasy or sci-fi books, or movies based on YA series, there are three things that a character needs to be consistent with.
1) Consistent within the movie itself - You might think this one is pretty easy to pull off, and you might also think that when I say "it's pretty easy to pull off" that I'm about to take a jab at Whedon. Ding ding ding.
When this is done right, it doesn't mean that a character doesn't change from the beginning to the end of the movie. No, that is a character arc, and it is good. It means that due to the circumstances of the movie, Han decides that he wants to fight with the rebels. It is Mystique slowly coming to realize that she has grown apart from her best friend and they no longer see eye-to-eye about mutants and humans. It is Katniss choosing to use her hunger powers for good and not for evil. (I have not seen Hunger Games.)
What it is not is when a character inexplicably changes their tone or mannerisms. Han is still a smarmy, cocksure smuggler, and not, say, a hopeless idealist or stone-cold killer. Creating an arc, and creating it well, is hard; Keeping a character consistent is not.
Which is why there are two lines in Avengers that ruin Black Widow's consistency. From the beginning of the movie (not even acknowledging the other films right now) she is cold, fully in control of her emotions, and very capable at getting shit done. Twice, she plays up the damsel-in-distress cliche to take advantage of her adversaries, once with the Russian gangsters and once with Loki. (I love both these scenes, actually, and I'll be talking about them later.) But, for reasons of sloppy writing and the fact that Whedon only knows how to script the same type of character, she ends up cracking-wise/complaining later on during the big dumb fight scene.
First she's fighting the aliens with Hawkeye and says, "This reminds me of Budapest!" and Hawkeye goes, "You and I remember Budapest very differently!" then the laugh track. Is joke.
Next she gets orders from Captain America to go up to the top of the building, and she has to whine about it. "Yeah, this'll be fun."
You're thinking these throwaway scenes of dialogue don't matter, and that, heh, Hulk punched the big monster. Well, no, changing your badass, tough, no-nonsense character, who faced any challenge given her with aplomb into a sarcastic, complaining girl is shitty writing.
2) Consistency between movies - I touched on this a little bit in an earlier, equally whiny post about The Avengers, and I want to talk about it more later when I go through each character individually, but, I mean, you get it. You're not dumb. If a character is one way in a certain movie, it's pretty awful to suddenly change them to another way, just because you think one scene might be cute.
I'm talking about this.
3) Consistency with the comics - I'm going to make a broad statement with two caveats: Consistency with the comics is not a concern at all.
But, if you change something so far from the source material that it is unrecognizable, then don't bother using it.
Just call her "purple hair girl" for fuck's sake.
Also what you come up with in your movie should be equally good with what's in the comics. The comics are a wealth of information. A lot of these properties have been published in comic form for 50 years or more. A lot of good writers and directors figured this out and adapted stories and ideas from the comics into their movies -- The Dark Knight, The Dark Knight Rises, X2 off the top of my head. Not only did directors swipe ideas from the comics, but in a lot of cases, improved upon them or at least didn't make them worse.
So, in this sense, it is important that I'm a fan of the comics. Things in the comics are not automatically better....
...they can add a dimension to a character or a story idea that sometimes the movie fails at.