The airplane that Shikishima flies is translated in English subtitles as a jet, but it's obviously propeller-driven. The translation is wrong.
The minesweeper crew claims to use a wooden boat because of magnetic mines, (which were designed to sit on the sea floor, not float). but the mines depicted are contact mines. However the character Kenji Noda states "We mostly handle moored mines" which they destroy by cutting their mooring cables then shooting them when they float to the surface.
The neighbor, Sumiko, gives Noriko some rice to make rice gruel to feed the baby. Babies can't survive off of rice gruel. They need formula or breast milk.
Shikishima lands his plane while still having a live bomb attached to his airplane. The normal procedure is to dump all live ordinance in the ocean before landing to avoid accidental detonations.
Normally kamikaze aircraft had their ordnance firmly attached to their aircraft. Many did not have the equipment to jettison the bombs, as they were designed as kamikaze weapons.
Pay close attention to the people during the rampage in Tokyo and you'll see various CGI doubles start floating as animation errors.
During the first dinner scene at Shikishima's house, baby Akiko is staring at the camera.
As Shikishima and the mechanics are doing last minute preparations on the Shinden fighter plane before departing, the mechanics and Shikishima salute each other. However, in the first VFX shot of the aircraft lining up for departure, you can see closely the mechanics saluting him off again like they did not before.