re: Do errors in movies take you out of the experience?

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.