When Kent, Jimmy and the woman look at the picture of Kent, it is impossible to be a double exposure. The camera, the kid has is a handheld reflex and there is no way he could get Kents body and face and Superman in exactly the same pose.
After Jimmy boards the subway to get away, the bad guys decide to set the subway to run on its own and crash, but that is impossible, because since the nineteenth century, there is a dead man switch in all subways and trains to prevent this scenario.
Superman disguised himself as a mailman where the uniform had a badge affixed to his hat and shirt. Mailmen were required to wear a badge affixed to their uniform hat only.
When Superman, disguised as a mailman, pretends to fall unconscious after being hit with the goon's gun and lands on his right side, the goon shoots at Superman who is now lying face down as opposed to on his right side.
During a tight shot of Superman flying, taken from an unusual angle, a wire is visible attached to Superman's left leg.
Near the end, when Superman removes his mailman disguise and jumps to fly after the villains, you can see his feet bounce off some kind of vault platform on the ground.