"I'm not a Trekkie, I'm just married to one" - my wife.
I liked the first two movies of the new series. I thought that they did a good job, with a clever premise to resurrect the series with a younger cast. I wrote in my review of Star Trek Into Darkness that the reviewers didn't seem to really get the movie. I find that to be a problem in general with reviews of science fiction films.
I read 5-6 reviews of "Beyond" before we saw it today. I mostly agree with them and for the same reasons. There is a lot of action in this film, the Enterprise gets cut to ribbons, (not a spoiler if you've seen any of the trailers), and perhaps the rescue mission and getting a derelict starship to fly again were a little beyond (get it) belief, but the director and the writers got a lot right.
What they got right were the characters, and this was mostly what the reviewers liked. The emotional heart and soul of the original show was always the characters, not the techo-babble, not the aliens, not even the Enterprise. Gene Roddenberry knew that right from the start. The producers of this series know that as well, and they do an exceptional job with the characters here.
A lot of Roddenberry's vision of a peaceful future shows through here as well. The central bad guy, Krall (played by Idris Elba with 20 pounds of rubber on his face) hates the Federation. He says "Your Union is what makes you weak". But Kirk and the crew of the Enterprise use their union as a crew to defeat him.
I also thought that the main story was resolved very well. Why does Krall hate the Federation so? It's not at all revealed in the trailers but it's a good, and believable, story. Also several character stories get resolved. Kirk, wondering what he's doing out in space; Spock, having to choose between his Vulcan heritage or staying with the Enterprise; the Spock-Uhura affair. Good, good, and good.
Some of the trailers show some fantastic architecture. These shots take place on Yorktown, a Federation built city in space, built into a sphere. You only get a glimpse in the trailers but the scenes of it in the movie are almost breathtaking.
Here's just one example of where the reviewers just don't get it. This is a minor spoiler if you haven't read any reviews. How did the the Enterprise crew use the Beastie Boys to destroy the alien drones? The reviewers were mystified. It was explained, with a lot of techo-babble to be sure, but it was explained. And the bit was set up much earlier in the movie. Dr. McCoy "Is that clasical music?" Spock, after a pause "I believe it is, Doctor".