The biggest flaw I think is that the film presents a creature that looks, sounds and moves like Godzilla, but acts like Gamera. He goes way out of his way, taking missiles to the face and tank rounds to the gut, but refuses to respond to the human aggression. He even makes eye contact with the human hero ATJ after ATJ saves Godzilla from the MUTOs by blowing up the MUTO nest. This totally flies in the face of the promotional material and interviews.
The second biggest flaw is that Godzilla should not need saving by a human. He shouldn't have been curb stomped by the two MUTOs. Even the first time he fires his breath weapon it was not a game changer, that was precisely when he got stomped to street level and then ATJ happens to blow up the MUTO nest and distract momma MUTO from stomping Godzilla's face in. Only after the two MUTOs were separated was Big G able to recover and lay the smack down with his tail to Daddy MUTO.
I agree the fight teases were annoying. It would have been better if Papa MUTO had simply flew away when Big G showed up at the airport. I also agree the film's plot should have been more Godzilla driven, even maybe an origin film, e.g. Godzilla Begins.
A few other nitpicks: That American supercarrier has multiple nuclear reactors on it. Why didn't the MUTO's try to eat it? Why didn't they use it as bait? Why didn't the MUTO's nest at Yucca flats? It is the most radioactive place on earth, perfect for a MUTO nest. It could have also made the final battle quite interesting being around Vegas, Nellis AFB, Hoover Dam, etc. Why didn't they use a nuclear sub as bait? They're full of nukes, plus the reactor. Ok, I'll stop being an Acolyte of Momus.
Overall, cool movie, I still like Godzilla 84 better though.