In the final scene where John is is about to conclude the ceremony a man with light pants and a blue top is walking from left to right in the background, when the close up is focused on Iris. The camera changes to John, the person walking is a completely different person, and the man with the light pants and blue shirt enters the shot now walking right to left.
As Oliver makes his speech before the final fight with the Nazis, Steel is seen with a helmet under his arm. However, he is never shown to be wearing one.
In the final scene when the camera moves from Iris to John, we see two people walking in the background. However, when the camera expands to overlook the pond, we only see one person walking along the path, where we should be seeing two.
Mr. Terrific points out that Overgirl has absorbed so much radiation that she is about to reach the Chandrasekhar Limit and go supernova. The Chandrasekhar Limit only applies when an white dwarf star reaches a mass approximately 1.4x our sun. Even if it was applicable to Overgirl, the resulting supernova explosion would have completely destroyed the earth, given the close proximity, not to mention most of the rest of the inner solar system.
Steel catches Supergirl when she falls from orbit, producing an explosive impact effect. While the ground directly beneath his feet is bare earth (as opposed to the grass around him) and there's a ring of dirt around them, the area where Steel is standing on is level with the rest of the ground and Steel's feet haven't sunk at all beneath the surface. At a minimum, his legs should have been driven into the ground by the force of the impact.
Several CGI shots in the final battle appear to be unfinished or poorly rendered, most notably Supergirl's face when she appears in the "hero line".
Maisie Richardson-Sellers accidentally slips into her native English accent aboard the Nazi Waverider, when she says "...but we don't know what we're looking for!".