I too had been waiting to see it, and now that I'm watching it, I'm being annoyed by a number of little things. Mild spoilers of little consequence ahead.
The biggest of the little things being probably people not reacting rationally to the rather important revelation of there being a goddamn monster. Like the guy knowing Godzilla is coming, and that the government doesn't want to evacuate, so he's just gonna sit there with his adopted family instead of taking everyone he cares about and running for the fucking hills.
And everyone's generally a bit too blase about the realisation that there exists a fuckhuge impossible monster in this world they're living in. Like, when the wife girlfriend roommate listens to his story from the war, the reaction I'd expect would be 'wait, you saw a what now??'. But she completely ignores it and is instead all consoling about his feels. (the most charitable, but never telegraphed, an interpretation would be that she thinks he's gone bonkers so she'd better not engage)
Also, the ruins are too pristine, the leads are too pretty, and every ship appears to have six people on it.
I get the monster is and has always been a metaphor for war, and I get the relatively tight budget, and the throwbacks to the classics, but it's not matching up to the hype imo. Like all Godzilla films I've seen, it feels cheap in all the wrong ways. At least Shin Godzilla had an audaciously designed monster - this one's very competently done, but by the book.
Bleh. Not sure I'll finish it.
Oh, and the people of Tokyo seem to be very fond of the Prometheus school of running away from danger.