Continuity mistake: In the prologue, the Nazis storm the Bresson residence. The elder Professor Bresson is sitting at his desk, back turned to them. There's an open fountain pen next to him, right by a paper sheet, but when Bresson answers rather defiantly to the bad guys, the paper sheet suddenly has disappeared. (00:02:15)
Continuity mistake: When Hodaka first fires his gun whilst being threatened by the man, the shell casing lands on the ground beside him, right next to his head. A couple seconds later, when Hina goes to help him up so they can run off together, the shell casing has vanished from the ground. (00:22:06)
Factual error: Towards the end of the movie when Superman and Henshaw are fighting on the Watch Tower in space, Lois hits the sun shades to lower them so that direct sunlight can hit Superman and power him up. This is out in space with no atmosphere to filter the sunlight. The reason the blockers were there was for this reason, to keep the harmful unfiltered sun light from hitting people on the ship through the windows. However, she is able to stand there in the direct light after it's done and kiss and hold Superman without being hurt or burned by the intense direct unfiltered sunlight or its radiation.