The worst Star Trek movie is Into the Darkness. It was lame and that's a fact. It was poorly put together and it obviously did not show appreciation for Star Trek fans and was like a slap in the face to us. Although some did like it, it was not well recieved by those who have been following Star Trek all these years. You would think it would have been the best one, and it should have been...but, clearly it was not. it was an insult. I, unlike most, didn't care for Beyond either. I felt it could have utilized the budget much better and that some of the scenes were expected and predictable, nothing of interest and it was hyped up way too much just as Into the Darkness was.
I, however, am not the authority on the subject but I think many true Star Trek fans share my thoughts here. The best one, in my opinion, was The Wrath of Khan. I felt it was great but it wasn't the most popular by any stretch of the imagination. Perhaps, that is what I like most about it and disliked about others. So, to each his or her own, I assume.