Many people have an aversion against science fiction “because it's not realistic”. For them, a movie (I'll stick to movies and tv series here, but this applies to any story) has to be consistent with the real world. If there are any space ships, lightsabers, monsters or elves the movie “does not make sense” and they quit. Let's call this kind of consistency external consistency.
Internal consistency is then consistency with the universe of the story. It's okay that Jedi have sword-like things while the rest of the universe use guns, because a lightsaber is clearly more useful for a Jedi. It is not okay if a movie pretends to be set in the here and now but, say, planes keep landing during a bomb threat on an airport.
Whether or not something is internally consistent also depends on how seriously the story takes itself. In Star Trek, for example, the transporter needs to break down, be jammed, be out of power or be stolen by the Ferengi every other episode, or they could just have beamed out of every dangerous situation. If the transporter was still online this would violate internal consistency. Doctor Who, on the other hand, often ridicules itself and clearly takes itself a lot less seriously. As a result pretty absurd things can happen without anyone caring: the story is itself a bit of a joke.
I don't care one bit whether a story is externally consistent. I like (some) science fiction and fantasy as much as anything else. But when a story is internally inconsistent, I start to dislike it pretty quickly.
This happend a few weeks ago when I saw Spielberg's “Close Encounters of the Third Kind”. Although it's not realistic that aliens would come to visit the Earth, I don't mind that. It's perfectly consistent with a story of, well, aliens coming to visit the Earth. The first thing that disappointed me, though, was UFO's being chased by police cars. What would you do if you were a UFO pilot, being able to move freely in all three dimensions, and you were chased by a police car on a road, being able to move only in one dimension? Saying that aliens are stupid doesn't cut it, because they clearly have the ability to build space ships. Also, if you're an alien race, trying to make contact, how can you have learned how latitude and longtitude work but not be able to say “Hello World”? And if you're a benevolent race, would you really kidnap people, shift them through time and throw them out nearly half a century later? All that does not make sense internally and made the movie quite disappointing for me. (Apart from all the strange things that are left entirely unexplained, but seem to be there only for the sake of overall strangeness.)
Of course this is not the only factor by which I judge movies. I don't mind a little bit of internal inconsistency here and there. I really did enjoy Casino Royale.