The big white building in Shinjuku that takes a beating from Mecha-King Ghidorah and Godzilla during the final battle is the main center for tax in Japan, which is why the audience cheered when it was destroyed!
This became one of the most controversial Godzilla movies. Shortly after the film's release in Japan, a cable news channel in America ran a lengthy story about the film's alleged anti-American sentiments. Scenes of US soldiers being killed by the Godzillasaurus were shown on the network, and the plot featuring evil Westerners from the future was debated. Director Kazuki Ohmori, however, defended his artistic decision on camera, arguing that the film was not in fact meant to be anti-American. Economic tensions between East and West were high at this time, and the negative publicity was very much a sign of the times.
When the time travelers arrive in February 1944, a US Navy officer sees their spacecraft, but his commander dismisses the possibility of a UFO; the commander then says, "You can tell your son about when he's born, Spielberg." This is an obvious reference to Steven Spielberg, whose father Arnold served in the war and whose war stories inspired the frequent WWII settings of his films.
For the army scenes, the production staff pulled every American (Geijin) from the military bases they could find. Many were working Japanese commercials at the time. For the army beach scene they chose the hottest day of that year and gave extras these very heavy wool uniforms and had them charging with guns blazing up the beach endlessly. At least three were overcome by heat exhaustion within the hour.
Columbia TriStar Home Video released Godzilla vs. King Ghidorah and Godzilla vs. Mothra on home video on April 28, 1998. This was the first time either film had been officially released in the United States. TriStar used the Toho dubbed versions, but cut the end credits and created new titles and opening credits for both films which was the first time it had that decision from Sony which it still happened on the 90's Heisei Godzilla films being released on video in 1998-1999, this print was still used on online streaming (Crackle), and the 2014 Blu-ray release.
Scheduled for the 50th anniversary of Toho, the film's original concept was going to be similar to Kingu Kongu tai Gojira (1962) and would have Godzilla face off against King Kong one-on-one. The film, which was to be titled Godzilla Vs. King Kong, never came to be because Turner Entertainment asked for too much money for the character King Kong; approximately 9 million US. So, Toho began to start production on Godzilla Vs. Mechanikong, the character that King Kong fights in Kingu Kongu no gyakushu (1967). However, Turner Entertainment still believed it was too similar to their character and asked for the same amount of money. In the end, Toho settled with reviving Godzilla's most famous foe, King Ghidorah, for this film instead.
This was the last classic Godzilla movie to be released theatrically in Germany, one of the very few Western countries where the franchise was otherwise moderately successful. Due to the low attendance and the distributing company going bankrupt soon thereafter, all later Japanese films were only released on home video or on television. It wasn't until the limited showing of Shin Godzilla (2016) in 2017 that a Japanese-made Godzilla movie hit German theaters again.
The trivia item below may give away important plot points.
The original Japanese trailer for the film oddly reveals two of the film's biggest twists. It reveals, both the future people's plan to attack the people from the present, and the reveal of Mecha-King Ghidorah.