"Star Trek Beyond" is standard-issue Star Trek. There are lots of costumes that aren't all that convincing. There is lots of danger that an evil genius might destroy the universe. There is lots of chasing and gizmo-tinkering that saves the universe at the last minute. It's all completely implausible and runs on arbitrary rules, but that's nothing new for sci/fi or fantasy movies.
The special effects of outer space and human habitation of it are higher quality than in the old TV show, of course. Starbase Yorktown is a series of rods radiating out from the center of a transparent sphere. Humans inhabit these rods, all of which appear to have their own gravity. There is no garbage in the streets and everyone is young, beautiful, and healthy, which is kind of creepy if you think about it too long.
The main characters perform their old tricks: Kirk is recklessly heroic, Spock is logical, Bones is crabby, Scottie messes with dilithium crystals, Sulu pilots the ship and is shown reuniting with his newly-minted male partner and daughter, and Chekov gets to joke about how a Russian invented something, a Cold-War-era joke that younger people won't understand at all, but that will give Baby Boomer Trekkies a chuckle. Of all the traditional cast members, Chekov is given the least to do. This is rather sad since Anton Yelchin, the actor who plays Chekov, died in a freak accident in June, 2016. There is also Jaylah, a space girl who looks a bit like Darth Maul. In TOS, Kirk was the most heroic. Not so here; everyone shines equally. Every participant wins a trophy. This insistence on making every character as heroic as Kirk lessens the differences between the characters and makes the interplay between the ensemble less fun.
The plot involves an evil genius who wants to destroy the universe, and the Enterprise crew stopping him.
Star Trek plots are always examined for possible societal significance. This plot may be a reference to The West v. Terrorism. In the beginning of "Star Trek Beyond" Kirk narrates a world-weary monologue. Life is too placid, too predictable. He needs a new challenge. This may be the scriptwriters, including Simon Pegg, who plays Scottie, voicing the post-WWII-era West becoming too comfortable. The villain of the piece, Krall, wants to re-introduce pointless violence and hate into an all-too-comfortable universe. Or maybe not. This is Star Trek; feel free to come up with your own interpretation.
The one character change in this reboot that saddens me most is Uhura. I loved Nichelle Nichols' Uhura. I loved her because she was an accurate depiction of a woman in a man's world. I also loved it that she was black. My family were immigrants and her minority status was an inspiration to me. She was a communications officer, the kind of job a woman would typically have. She was in the background, as women often are in men's stories. She was someone I could embrace, relate to, and be inspired by.
In the reboot, Uhura is not really African American. Zoe Saldana is a light-skinned Hispanic. Uhura's difference has been toned down. And Uhura has become a leader, an action hero, as karate-happy as Captain Kirk. Conversely, she spends a good amount of her time playing a stereotypical role assigned to ethnic women. She is the hot, exotic temptress who will lure cold Spock into a love relationship. The original Uhura's sexiness was never exploited in this way.