Do errors in movies take you out of the experience?

Depends how bad the error is.

Something like using parsecs as a measure of speed in Star Wars doesn't bother me much at all.

The terrible fighting by the extras in Dark Knight Returns? That's really pushing it.

Complete disregard for rules in sports movies? FML.

Oddly enough, the one that bugs me the most is the way movies and TV portray how local news broadcasts and live shots work. It drives me nuts to see a "live shot" in a move where it's just a camera guy and a reporter w/no production truck, no lights, no cables, and a reporter running up and talking to a random stranger to ask them what's happening. Maybe it's b/c I used to be a news producer so I know how it all really works but that's the one thing that will instantly take me out of a movie.

Like what kind of errors? Continuity?

Some do some don't, just depends on the movie- mores specifically how serious the movie is taking itself.

In a comedy like Got Tub Time Machine or The Mask it doesn't bother me at all.

In a dramatic period piece like Gangs of New York or Titanic or Pearl Harbor it is pretty distracting. That's probably true of most period piece (definitely not all- Ben Hur and The Good, the Bad, and the Ugly are two that have stood the test of time)

In movies like Armageddon or John Wick or Smoking Aces- which have serious subject matter but approach it with a degree of levity, I'll notice but not necessarily be bothered by it.