The Iffy: Phantom Drive
The Phantom drive was originally used to exile the leaders of Zod's rebellion into the Phantom zone, an interdimensional prison. But Zod re-kajiggered (technical term) the machine into a hyperdrive, because apparently that is really easy. What is this drive, which can both open dimensions and be used as an interstellar spaceship? It seems to be conveniently multi-purpose. There was some unconvincing technobabble about how the Phantom drive bends space, but the movie never quite established how Kryptonians have amassed such a huge interplanetary empire or, for that matter, how baby Kal-El's ship got its precious cargo to Earth. We don't expect them to show us a mathematical proof, but it always helps to know what breed of as-yet-fictional space travel is being utilized, especially when it's such a huge plot point of the movie.