These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: It's Akira Ifukube on top form. Some of the library cues inserted for the American version aren't bad either, especially the clinic shootout track, which was rather unsuitably scored with Godzilla and Rodan's theme in the Japanese cut.
Broken Base: In America, fans are divided over which is the best Ghidorah, and it generally comes down to 3 of them- The Heisei Ghidorah, the Ghidorah from Rebirth Of Mothra 3, and the original which features in this film.
Complete Monster: This film introduced audiences to to Godzilla's archenemy, the titular three-headed dragon, and living catastrophe, King Ghidorah. Reveling in the destruction that he causes, King Ghidorah flies from planet to planet, exterminating life for his own entertainment. Having already annihilated the civilisation on Venus (Mars in the dub), King Ghidorah arrives on Earth, intent on repeating the process. Beaten by Earth's protectors, Godzilla, Rodan, and Mothra, King Ghidorah did not accept his defeat gracefully, and returned again and again, ravaging the Earth on behalf of the Xiliens in Invasion Of Astro Monster, the Space Hunter Nebula M aliens in Godzilla vs. Gigan, and finally the Kilaaks in Destroy All Monsters, which proved to be the Great King of Terror's last stand. Essentially a life-hating demigod in the form of a dragon, King Ghidorah was undoubtedly the very worst that Godzilla's Showa Era Rogues Gallery had to offer, and was responsible for the loss of millions of lives.
Subverted, as the second Ghidorah movie, Invasion Of Astro Monster, while although lacking in the grand slam monster spectacle of its predecessor, is often considered to be a better written and cohesively assembled science fiction story, plus it had the benefit of actually being released outside just the U.S. and Japan.
Germans Love David Hasselhoff: Owing to its regular theatrical and afternoon TV showings from the mid-sixties to late-seventies, the film has a somewhat large American fan base, as it was only shown stateside during its original release, but nowhere else, so foreign viewers who got the debatably superior Invasion of Astro-Monster in its place are mostly indifferent or actually dislike it.
Moment Of Awesome: The Battle Royale at the finale is awesome (even if it is a little too goofy at times) and is still among the most iconic battles in Kaiju eiga and a turning point in the development of Godzilla himself.
The sequence where King Ghidorah devastates Tokyo is also great stuff and makes very other scene of city destruction before it (and most after) look like a picnic- nothing has been quite as grand
And of course, Rodan vs Godzilla, where the pterosaur actually goes toe to toe with the King of the Monsters.
And when Mothra convinces them both to get their heads out of their asses and battle King Ghidorah.
Narm: When Ghidorah causes a rockslide that kills Malmess, he... catches a giant rock, then falls to his death.
The English version, dubbed by a-Bellucci Productions!, while praised by some, has its fair share of narmy lines, many delivered by the princess.
"I think that bracelets are worthless and silly. If I had one, I'd give it away immediately."
Narm Charm: Rodan throwing rocks at King Ghidorah to defeat the Eldritch Abomination is goofy as heck but somehow awesome.
Squick: Rodan drops Godzilla crotch first onto an electric tower.
Ugly Cute: Mothra Larva, and in a sense, Godzilla.
What Happened to the Mouse?: The second Mothra Larva from the previous film Mothra vs. Godzilla disappears without explanation. Officially, we don't know what became of the second larva. In the Japanese version, the Shobijin explain that it died (likely from the beating it received being whipped around by Godzilla's tail).