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.
In the first two acts, Godzilla destroys multiple boats, destroys a village during a typhoon, and attacks Tokyo twice, thoroughly destroying the city in the process. In the final act, Godzilla is... resting in peace. To him, it may be the fact that Humans Are Bastards and conducting nuclear tests which may have scarred him for life. His successors even sees humans this way.
Godzilla, having vented his revenge and left his message to man, is now content to live in the sea.
Anvilicious: This is a film about the bomb, and it's not at all subtle about it. Godzilla is born from reckless nuclear testing, and, like the atom, proves a dangerous and unstoppable force far outside man's control. Furthermore, Dr. Serizawa's anguish over potentially developing the next superweapon and struggle over using it has obvious overtones for the atomic age. The film closes with Dr. Yamane solemnly predicting that future atomic testing and brinkmanship will only create more monsters.
Some Anvils Need to Be Dropped: Subtle? No. Effective? Fairly. Something the world needed to hear in the face of a new world war fought with nuclear weapons? Without a doubt.
Awesome Music: The escalating main theme perfectly underscores a unstoppable force of nature.
When you have a Godzilla theme that sounds like this, then you know it's not the cheesy giant monster movie the later films became known for. It's a straight-up sci-fi/horror film with heavy emphasis of nightmare fuel and tragedy.
Ear Worm: Since this is Akira Ifukube's first film in which he composed, many themes, all the music in the movie are friggin' earworm-worthy. Especially the sad themes.
MST3K Mantra: As the commentary brings up, there are several aspects of the film that you have to ignore in terms of reality for it to work, like the following.
If a giant dinosaur got hit with a hydrogen bomb blast, it would probably just kill it.
Why would a hydrogen bomb give a dinosaur atomic breath and invulnerability to weapons (remember, this was made 9 years before the first X-Men issue, so the idea of mutant superpowers wasn't in common consciousness yet)
A weapon that destroys oxygen doesn't kill everything in the water, it just creates a lot of hydrogen.
You can't destroy an element, so the weapon in itself is impossible.
The fact that the weapon simply stops working within Tokyo bay instead of spreading and affecting all water in the world as it logically would.
And finally, why the monster seemed compelled to keep attacking Japan when other islands are relatively nearby.
Especially considering Japan wasn't the one to set off the bomb that woke it up in the first place, America was.
Narm: When Emiko is shown Serizawa's experiment, she looks away and is accompanied by a sound that is supposed to sound dramatic but sounds more like the composer fell asleep on the piano.
Nightmare Retardant: Despite the often primitive effects, the scary parts of the movie work remarkably well, except for... Godzilla's hand-puppet closeups. His unmoving, shriveled arms are in a constant "about to give a hug" position, and he has Fish Eyes. Combined with the low angles that sometimes make his mouth look like a smile, he looks like all he wants is to hug every building. In another occasion, he turns his head to the side, and ends up looking like one of The Muppets.
Older Than They Think: When people think of Godzilla, they refer to the Showa era films, only to overlook this film, which is made in 1954. And thus, any articles about this film will usually be referred as Godzilla (1954).
The famous "In Pursuit of Godzilla" theme stems back further in Ifukube's courier, as part of his 1948 violin concerto. This early rendition can be heard in the main titles of this film: http://www.youtube.com/watch?v=NklvxiHk6sE
Old Shame: Ishiro Honda expresses that he lamented the fact that most people gained ire of the film because of its imagery. Now, it's one of Honda's best works of Kaiju from fans.
Special Effects Failure: A few scenes. Scene one: A military platoon attacking Godzilla, a solider oddly moves his head in a strange matter. Scene two: A window close-up shows Godzilla's tail. You can see the overhead wires near the tip. And scene 3: The Diet building is seen crumbling twice.
The use of toy fire trucks (manned by very obviously toy firemen) coupled with the sped up footage during the attack on Tokyo scene is very, very obvious.
The Circular Drive used to show the firetrucks marshaling to prepare for the attack is just as obvious. There's only one truck!
During Godzilla's attack with the train, during a close-up of the legs, you can see the suit folding while he's walking.
True Art Is Angsty: Fans very often use this film as an excuse to gain the franchise respect in snobbier circles.
What an Idiot: So Godzilla has been found out to be the cause of the ships gone missing.
You expect: The government officials to listen to Dr. Yamane when he clearly points out no conventional weaponary can kill Godzilla, and he absolutely hates lights.
Instead: They try to kill him in the sea (which clearly didn't work), ignore Dr. Yamane's fact of Godzilla being immune to conventional weaponary, have a small platoon to deal with him in his first raid, bombrding the thing when he crosses the electrical towers, and continue attacking him when he has a Breath Weapon. All the course of the second act. Let's not forget they were waving their lights when he surfaced.
Vindicated by History: Prior to the debut of the film, the film received very negative reviews due to its Too Soon and Nuclear Weapons Taboo imagery. However like its American counterpart King Kong in Japan, the film was highly praised in America in 2004, where it gained two DVD releases by Classic Media and the Criterion Collection.
Awesome Music: Lots of it, but From Mars to Sirius generally seems to be the band's most highly regarded album.
Fandom Rivalry: With Meshuggah. Although it has been often regarded as the "Metallica vs. Megadeth" of tech-death, the bands' fanbases have both shades of rivalry and friendship.
Magnum Opus: L'Enfant Sauvage and the abovementioned From Mars to Sirius.