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: Takayuki Hattori provides a rather nice music score. While it isn't as exciting or memorable as the works of Masaru Sato or Akira Ifukube, Hattori's score is quite serviceable. The track End Title: Godzilla - Dreaded God is particularly good, with its vocals giving a sense of awe for the title character. One thing that is nice is that the American version of the film placed Godzilla's roar at the end of the track, making it sound even better.
The music for the Japanese version of the final battle between Godzilla and Orga was completely rewritten for the American version. The music in the latter is a big improvement, and makes the battle far more epic and exciting.
Foe Yay: Kataragiri while wanting nothing more than to destroy Godzilla, is awed by seeing him face to face and up close. Godzilla kills him though.
Harsher in Hindsight: This line from Yuki after hearing that Godzilla is making his way toward a nuclear power plant. About twelve years after the film's release, the Fukushima Daiichi nuclear disaster happens following the real-life Tōhoku earthquake and tsunami.
Nightmare Fuel: The manga adaptation. After the Millennians restrain Godzilla, the main characters and Godzilla see what appears to be Millennians assimilating people, as seen here.
They were growing bodies of their own, which makes their faces all the more horrifying when they start mutating into one horrific being.
The Japanese cries of the Millennian alien are oddly more abrupt, piercing and scary than the sounds in the U.S. version.
Special Effect Failure: The movie experimented a lot with Chroma Key to project Godzilla onto real-life footage instead of having him trample over miniature environments all the time, and while some shots pull it off, there are many scenes where the colors and shadows don't match up, or where he appears blurry while the rest of the shot is crisp — worse, in one of the shots, his feet simply disappear into the ground for no reason.
Many scenes with the CGI version of the Millennian ship, thanks to its incredibly flat texture. At one point, it is shown reflecting the city lights on its underside, which makes it even more obviously fake when the camera pans to its non-reflecting top.
For several effects shots that required the film to be sped up digitally, grossly unprofessional frame ghosting rears its ugly head.
Strawman Has a Point: Though Katagiri jumps off the slippery slope when he tries to blow up a building that he knows Shinoda is in, he initially has a fairly reasonable position: Godzilla must be destroyed because he always causes massive damage when he shows up.
Woolseyism: The U.S. looping team handled writing very well and changed some questionable terminology from the Japanese script (Organizer G-1 becoming Regenerator G-1), and entirely overhauled the exceptionally poor original export dub they were given to work with.