Factual error: About 11 minutes into the film, Luthor's yacht is seen in heavy seas in the Arctic. The helo on the helo deck has its rotor blades extended. This would cause immediate damage to them so is never done, even on carriers - the helicopter wouldn't be able to fly properly. (00:11:20)
Factual error: The shuttle attachment to the plane is wrong - the shuttle undercarriage would not be part of the fixtures. Not only that, when we see the undercarriage raise into the shuttle there are no wheels, so the shuttle would not be able to land upon its return, also the the undercarriage poles change shape before and after release.