If it took a gigantic rocket to get the space capsule in orbit around Earth, how was it then possible to shoot the landing capsule from Earth 2 up into orbit without another gigantic rocket to launch it?
They talk about the possibility of the astronauts having turned but orbital mechanics make this impossible for a spacecraft with limited fuel. They would have to go a full orbit around the Sun or use an immense amount of fuel - much more than they could have possibly brought with them.
The protagonist is surprised by a driver on the wrong side of the road but he does not even mention the fact that the steering wheel would be in the other side of the car than what he is used to if everything is reversed.
When placing the astronauts in the capsule, we see Roy Thinnes facing us on the left-hand side and Ian Hendry on the right-hand side of the capsule. A few seconds later, the positions are reversed and remain so throughout the scenes involving the capsule.
The goof item below may give away important plot points.
Col. Ross uses a lander/ascent module from the "mirror" Earth to recover the mother ship from his own Earth in order to prove the existence of both worlds. There was concern that the electrical polarization (right-hand rules, etc.) would be different for each vehicle. Since this could potentially pose severe consequences for both vehicles, then why did Col. Ross attempt to physically dock the two vehicles (with the predicted result)? Surely it would have been more prudent to park the ascent vehicle a short distance away and space-walk the remaining distance.