Okay, I saw it a second time last night and I'm ready to give something like a coherent appraisal. The movie had so much hype behind it for me that honestly my first viewing was somewhat numb, but now that I've seen it twice...
My appraisal is that the movie is quite bad.
Part of the problem is with the script... characterization... stuff like that. The other problem is with presentation; in the style and execution of the monster effects sequences and editing in general. In both respects, this movie is weak, meaning that neither one can rise up to save the movie and supplant the other whenever necessary to make it entertaining or enjoyable.
The central fractured family has a great introduction (I'm a big fan of the kitchen scene that appears to be a normal American house, but pulls out to reveal the location as in a dense rainforest next to an ancient temple) but once they're introduced they spend most of the time running around and yelling and not developing their characters sufficiently forward. Vera Farmiga is especially disappointing, because her arc could potentially be very interesting, but it's sketched in so basic a fashion it's hard to get invested. Millie Bobby Brown is fine in the role, but is given very little to do, especially considering she was touted as the lead since the beginning. Kyle Chandler's character is probably the most fleshed-out, but it's also very cliche, of a long line of sad dad characters that have populated recent cinema, and reminiscent of better characters Chandler has already played. He ends up being an annoying grump. Ken Watanabe is amazing at delivering ridiculous lines in a grave manner, but considering that's the only thing he's asked to do the one-note nature of it wears thin pretty quickly. The eco-terrorists are annoyingly underdeveloped. Charles Dance does try to add a bit of high camp to his performance, but he never goes all-out into Langella Skeletor territory, which would have been most welcome in my opinion! As for the crew of G-Force... I mean, as for the crew of Monarch, they represent the exact wrong execution of an Ultraman defense team. You know how in a good Ultraman show the defense team members have personalities that complement and bounce off each other well? Well, here they're a bunch of idiots that provide a bunch of exposition yet can never make a good decision unless Kyle Chandler's character can give the common sense solution to whatever problem they have that they, despite having seemingly all the great scientists in the world, just can't see. It's annoying as all get-out! It's an airship full of idiots being bossed around by a grumpy Kyle Chandler. Perhaps the scenario could have been mined for comedy, but the one-liners here are quite tepid. At least Bradley Whitford is somewhat amiable, even if most of his jokey lines are groaners, another one playing a pale imitation a better characters they played in better films.
The story is so chaotic that nothing can be developed sufficiently. It's hard to get invested in something when everything is just flying by. Something like the Oxygen Destroyer has little impact; introduced, implemented and forgotten about so quickly only a fan recognizing it as a callback could possibly remember it even happened at all.
And let's talk about all the callbacks; the fanservice. I found it pretty annoying, to be honest. I resent being expected to applaud something just because I recognize it as familiar. It's not enough that something familiar be plugged into a story; it has to be twisted somehow or developed naturally in the story itself so that even new audiences can appreciate it coming in cold. What's the use of replicating certain shots from old movies if the movie fails to understand the storytelling function those shots had in those movies? It's bizarre. It's like in Arthur C. Clarke's novel of 2001, when Dave realizes the room he's in isn't a room for a human being to actually dwell in, but rather something like a sculpture made by the alien intelligence based on images of human rooms. Godzilla: King of the Monsters is a sculpture of a Godzilla movie made by someone very familiar with them without the understanding of how even some of the most basic one's work.
But, at the very least the monster scenes are worth it, right? Sadly, I found most of them quite poor. There are excellent, beautifully composed shots of the monsters which have largely been seen in the promotional material. But taken as whole sequences in the film these scenes are undercut by certain bad technical and creative choices. First of all, almost every shot of the monsters is only a few seconds long only to cut to human reaction shot of equal length before cutting back to the monsters. This disjointed approach makes it very difficult to appreciate the fights as fights. Fights are storytelling, they must be followed and understood. These fights are a barely connected sequence of things that people thought were cool shots or moments without the care of being cohesive storytelling. They're also undermined buy inconsistent framing and shot choices often revolving around having the human heroes being directly underfoot of fighting monsters and miraculously (mostly) being able to make it out relatively unharmed despite the fact that even the most generous audience member would expect instant death from this close proximity. It makes the drama less dramatic when we can't buy the peril and it awkwardly effects our perspective of the monster battles so it ends up making the sequences seem even less realistic then the most basic man in suit fight! Unfortunately, it feels like Doigherty is trying to replicate the tricks Edwards used just such great effect at the end of the 2014 film, which just goes to show what a meticulous, even brilliant visual storyteller Edwards is.
The monsters, in personality and character, are all fun. I don't have a problem with that. It's great to see Rodan being badass again after spending the majority of his career demoted to a second banana who never got a chance to shine like and his 1957 film. Godzilla is maybe a bit too close to Gamera's characterization for my taste. King Ghidorah comes off as more of a jerk then as ultimate evil, but honestly that's probably more interesting in terms of something the audience can wrap their heads around. Mothra is appropriately mystical, even if the movie tries to couch everything in something plausible sounding.
That's another problem I had: the film is so over-the-top but always keeps pulling its punches by explaining how plausible whatever is going on is. If they just said magic exists or King Ghidorah was exerting a psychic influence on the human bad guys imagine how more simpler and understandable the plot would be! Maybe the bad guys are aliens who want to destroy the human race? There's a reason Toho keeps using that plot: it's clear and understandable! Not everything has to be overcomplicated and over-explained. That doesn't make something more sophisticated or modern, it just wastes the audience's time.
And, as has been said before; the inversion of having Serizawa sacrificing himself by reviving Godzilla with a nuke to save the world is a certainly unintentional but nevertheless terrible middle finger to the themes of the characters of both Godzilla and Serizawa, as well as of the franchise overall. It turns out nuclear weapons are great! Glad we sorted that out. Even Godzilla vs. Megalon and Final Wars gave better respect to the central metaphor! And to have it done by the one Japanese member of the cast... it's so ignorant it's almost amazing.
But, to wrap up with some positive notices - I like the introductory scene with Rodan. I like both of Mothra's birth sequences. I love that we finally got the Godzilla rock song in the end credits. I got emotional because of the picture of Nakajima in the end credits. I also liked the design of Godzilla's underwater temple, even if I dislike the scene itself. It also holds true to the tokusatsu tradition of showing us something really cool just before wrecking it.