When Superman takes off to fly after the bus, there's a quick cut to Superman leaving the ground (on wires, not the later jumping take-off), and it's obviously a stunt double. In an early episode during filming, George Reeves was doing a similar stunt himself and the wires broke, causing Reeves to fall to the ground and hurting him badly. He refused to hang by wires after that.
Lois Lane's car is a 1950 Nash Rambler Convertible Landau Coupe.
Although the investigative committee is being broadcast only by radio, it is never explained how the crooks can see the person the committee is questioning in order to use their mind machine.