Continuity is kind of a make or break thing for me because I like settings almost as much as I like stories. Hell, I buy RPG manuals that I know I'm never going to actually play just so I can read about the setting.
So when a corporation (let's face it, it's almost always a corporation) comes in and mucks up the continuity, I start to lose interest real fast. I mean, Star Wars already had an absurd number of levels of canon [http://starwars.wikia.com/wiki/Expanded_Universe#Official_levels_of_canon], then Lucas made the prequels, and now we're going to have a split post-Jedi canon and... the setting is ruined. The stories might be good, the characters good, but the setting, without any sort of internal consistency, is ruined, and I have no further interest in it.
And this isn't the first time I've "broken up" with a series because of continuity problems. I dumped Dragonlance after reading over 100 books because not only did some books directly contradict others, but some books actively made fun of the others. It's like there wasn't any editorial oversight at all, and authors just mucked around as they pleased without respect to those who came before.
This is also why I can't really get into comic books. I mean, sure, Marvel has better continuity than DC to an extent, but they still retcon the Hell out of everything to the point that no one really knows what has and has not happened or what the rules of the setting are at any given point in time. Once you get into the cross-medium stuff (books vs. movies), even a token nod to consistency goes out the window.
In summary, I primarily read single-author (or cohesive team) scifi and fantasy because everything else drives me up the wall.