Goofs

Chapter Seven: The space radio, which Buck has difficulty moving, is picked up by Buck as if it were so much balsa wood.

In Chapter 1 "Tomorrow's World", when the dirigible crashes and Buck is seen passing out, the exterior door is closed. When the rescuers are melting the ice from outside (The camera view is from the inside looking out.), the door is already wide open.

When communicating between the Earth and Saturn by radio, the conversation is depicted as if they were talking locally. In reality, it would take radio waves a long time to travel between the two planets.

Saturn is a gas giant, not a rocky planet.

Despite having breathable air and normal gravity on Saturn, it still seems odd to see Earth and the Moon in the sky as part of the Saturn exterior shots. If that were so, Saturn should be readily seen, as well as its rings and moons as part of Earth's sky.

Chapter One: When the officer picks up the dog that is supposed to be in suspended animation, it slightly lifts its head, opens its eyes, and an ear moves. While on the table, the dog can be seen blinking. This is all before a character feels the dog's heart and announces "it's starting to beat".

When Buck and Buddy infiltrate the council on Saturn, the second soldier reacts to being shot by Buck's laser gun before he is shot.

Chapter One: It was never explained how Buck, just arrived in "The Hidden City", learned to fly a spaceship and the use of "modern" equipment.