Translation:I went to the movie theater with my brother.
It's being picky about your English I think. Movie as in, the actual moving pictures that you watch, is 'película', where as, the theater you watch the movie in is 'el cine'. In English (where I live in the States at least), we often say 'the movies' when talking about the theater itself. So it will accept 'movie theater' singular or 'movies' plural, but not 'movie' by itself.
True if you are talking about I went to the movie theatre to watch any movie(s) in general. What if we talk about THE/THAT movie (say Spider Man), I went to (see) that movie. You could not fault people for such situation. Don't tell me you never had a movie in mind when going to the theatre.
Technically there is no grammatical difference. "Theater" is just how we spell it in America. Most other English speaking countries spell it "theatre."
However, when you do see it spelled "theatre" here in the US it is usually attached to the arts (a play, an orchestra, etc). This isn't a rule, it's just the venue's way of sounding more artistic. Basically, whenever an American wants to sound "fancy" or more formal we start phrasing things the way Brits do. :)