this should be right with today at the beginning or end.

I think "Let's go to the movies today." should also be accepted. "Let's go to the theater today." sounds very British, as an American I would never say that.

극장 = 劇場

It says is wrong just because I didn't put the period at the end.

You really need to decide what 극장 means. I've been pinged for translating it as both "theater" and "movie theater" in different sentences.

These exercises are very inconsistent with the use of the word "together." In many cases, it is simply implied, but in other cases, it is actually necessary as part of the response. :(