Just before the crook throws the lit stick of TNT in the safe with Frank Smullens and closes the vault door to blow him up he tosses his hat in with him. The hat falls flat on the floor upright. When Superman arrives moments later and looks in the vault with his x-ray vision the hat is on it's edge leaning with the top against the safety deposit boxes. Then when Superman pulls the vault door off and retrieves the TNT the hat is on the other wall perpendicular to where it just was and with the top of it now facing outward.
When Superman looks at Smullins through the vault door, he sees a stick of dynamite whose fuse has burned down to only a few inches in length. After Superman removes the vault door and takes the dynamite to dispose of it, the fuse is considerably longer than it was before he got to it.
Early on, when Clark Kent says he needs to get the heel of his shoe fixed he opens the door of Perry White's office but there is no door latch or striker, revealing the door to be a prop.
When Olson and Celia are tied up, the hoodlums then open two natural gas valves. Superman appears and disables the hoodlums, then immediately departs. Smullins and Lois then rush in and Smullins 'saves' the day. The entire time this is occurring, natural gas is filling the room from the open valves that no one ever closed.
When the crook unlocks the bank vault door and opens it there is no latch on the door.
When Jimmy speaks his story into the microphone in Perry White's office, the reels on the tape recorder aren't moving.
When Superman flies at a downward angle, the clouds in the background are at the same angle indicating that the horizontal camera image was just tilted.