https://archive.org/details/CharacterInsightEp199
Star Trek Beyond added a new writing team and a new director Justin Lin after Into Darkness came off as a little stale for the new crew, and these changes proved to be well worth it. There are great visuals without the crutch of lens flares, most notably the incredible scenes on the Yorktown station, and the soundtrack is once again fantastic, just like with the previous two movies. The slower character scenes, particularly those with Spock and Bones together, and those with Scotty and Jaylah, were outstanding as well, albeit with the same high amount of callback lines, references and cheesy humor as before.
Ironically, this may be a better homage to The Wrath of Khan than the plagiarized version presented in Into Darkness was. The villain turns evil and against the Federation based both on his nature as a soldier and as a result of being stranded without rescue, which sounds a lot like Khan's original story arc! But it's a believable villain, and while the clues are there throughout the movie, it's not written as obviously as things like the "Magic Blood" in the previous movie. Plus Idris Elba continued the trend of great villain actor performances set by Cumberbatch 3 years ago, particularly when he got to finally act outside the rubber suit of the Krull character.
The movie is not without some minor faults. The story is painfully slow at the beginning, which may turn some non-Trekkies off after the fast action of the last two movies. The hand and gun fight scenes fall very flat compared to the space battle scenes. The Enterprise is abused to death once again as a cheap way to build tension, but perhaps this is a fitting homage to the original third Star Trek movie, where Kirk flirted with being an admiral and the Enterprise-A was born.
My only other complaint is that the story felt a little generic in some spots, with evil powerful villain trying to obtain a Tesseract-like object and then use it to destroy the world, forcing our heroes to go pursue that Tesseract...I'm picking Guardians of the Galaxy terms for a reason. It's enjoyable as a different story for a Star Trek movie, but it's somewhat stale as a modern science fiction or superhero movie plot.
Where Beyond moves to the next level, however, is the "big philosophical and life questions" which the crew tackles around all the action scenes. This was Roddenberry-style science fiction at its finest, making you think as much as be in awe. By moving the crew three years ahead into a deep space mission, this story was able to stand alone with its own big questions about unity and motivations/purpose in life, while moving away from the crutch of Earth or other known worlds.
Plus, the tributes to Nimoy, Yelchin, and the original crew from the 25th anniversary milestone were outstanding. Hits you right in the feels.
I think this movie is and will remain a top 5 Trek movie, maybe Top 3 based on your preferences.
I count myself incredibly blessed to be able to enjoy well made Star Trek and Star Wars in the theater with my 7 year old daughter, as those franchises didn't put out much great movie content during my own childhood. Seeing the magic through her eyes and making the next generation of Trek fans is an outstanding way to celebrate the 50th anniversary of this IP.