The ejection seat installed on the Shinden fighter is of German design judging by the German writing on it. This makes sense because Japan never developed ejection seats during World War II but some late war German aircraft featured early versions of this technology. Germany also transferred a number of aviation related technologies to Japan via U-Boat during the war, so it's likely they were planning to install the German made ejection seat on the prototype Shinden when the war ended.
Godzilla's extremely territorial behavior likely explains why he initially attacked the airfield on Odo Island. The airfield was obviously a fairly recent addition to the island and the increase in human activity surrounding it caused Godzilla to instinctively target those he viewed as trespassing on his turf. The native islanders likely knew enough about Godzilla to avoid angering him or at the very least head for the hills whenever it was clear he was in the area. The same can't be said for the garrison who continued with their usual activities despite a number of warning signs of the monster's approach.
The minesweeper boat Shinsei Maru has the kanji 新生丸 painted on it, where 新生 shinsei meaning "rebirth" matches well with Shikishima and his crewmates having a new life post-war, and as well being the sixth film to be a reboot from the original 1954 film's origin point.
The operation being named "Wadatsumi" by Noda is rather fitting, as Wadatsumi - alternatively "Watatsumi" - is a Japanese sea dragon deity, given how Godzilla has occasionally been worshiped as a sea god in some lore.
Captain Hotta is introduced as having commanded the destroyer Yukikaze during the war. Yukikaze was famous for surviving some of the most intense Pacific War naval battles nearly untouched that many Japanese ships never returned from, so it's fitting that he leads a desperate effort to take down Godzilla where most of his men actually survive.
Film director Yamazaki has stated he considers Godzilla post-mutation as a Tatari-gami, or "curse god". In the ending we see Noriko's neck has an ominous black growth moving across it. For "killing" him, the monster cursed Shikishima by infecting the love of his life with Godzilla's cells. This emphasizes the monster casts a long shadow over Shikishima, that he'll never be free of.
Godzilla's atomic breath is so powerful that it scorches even him, with charred wounds inflicted onto his body each time he fires the breath. The film's themes are about how war and hatred is destructive to one's self, with Godzilla as an incarnation of post-war trauma: but it adds an extra layer of metaphor to see the film's titular antagonist actually destroying himself with his own attacks—which he doesn't stop using more than once. His hate for humanity trumps even his own physical well-being.
Pay attention to Godzilla's spines whenever he was charging up his atomic breath in Tokyo. Notice how they extend out before slamming back in? It's like the hammer of an atomic bomb triggering its nuclear explosion.
The novelization reveals that Godzilla was irradiated in the Baker Test of Operation Crossroads, which was the second of two atomic tests carried out at Bikini Atoll. This likely explains why Godzilla was in that area in the first place, as the US military had just carried out the Able Test prior to Baker. Godzilla is shown to be highly territorial and will respond aggressively to anything he views as a potential challenger. The unfamiliar sound of Able going off likely drew Godzilla to Bikini Atoll, ensuring he was close enough to the followup test to receive a high dose of radiation.
As this Twitter user points out, when we see Godzilla for the first time at the Japanese garrison, his movements are very fluid and animalistic. Then, after he receives his mutations from the atomic bombs, his movements become much more stiff and robotic like. It's like his mind can't catch up to the drastic changes to his anatomy and size increase; he doesn't know how to move in this "new body." This issue is only really "solved" whenever Godzilla is in water, because at least the issue involving his mass is mitigated, and as a mostly aquatic based creature, he can move more comfortably in there.
- alternatively "Watatsumi" - is a Japanese sea dragon deity, given how Godzilla has occasionally been worshiped as a sea god in some lore.