Plot hole: While still unsure where and when they are, the Nimitz has two F-14 Tomcats aloft, investigating a pair of low-altitude radar contacts. They determine the planes are WWII-vintage Japanese Zeros in full military livery. The Tomcats are told to shadow the Zeros without engaging them. Then, the Captain, the XO, the CAG and Lasky all go to a formal dining room and sit down to tea. In this scene, they talk about many other 1941-era things that are happening, but nobody mentions the Zeros. That fact, and that they left their Tomcats where they did, suggests this scene was meant to be in an earlier part of the film (when things seemed odd, but no imminent threat existed) and got moved here, creating a plot hole that the USS Nimitz could slide through sideways. US Navy nuclear carrier command staff wouldn't simply go have tea under the current conditions. (00:40:30)
Plot hole: Lois and a friend of hers are watching Non and Superman fight. But this is totally senseless, because Superman had been flying around Metropolis and chances are slim that he appears in the very same spot to let Lois watch him. And, second and most important, should any doubts arise, the panning angles of the camera never show Lois's building, with the big broken window and the flag poles.
Plot hole: Antoinette Lilly makes headlines as being murdered and her husband is charged and sent to a criminal asylum...despite the fact that no body has been found and no one has even bothered to go to the hotel or town she was last at to investigate whether or not she's alive or dead. Not believable.
Suggested correction: John was framed by Antoinette's step-mother (who stood to gain Antoinette's inheritance). People have been arrested for murder without a body being discovered first though. Additionally, we find out that the lawyer who helped framed John also paid him to confess to the crime and admitted to being mentally unstable. So nobody was even trying to look for Antoinette.