Like 2001, which came out 18 years later, Destination Moon is an accurate depiction of space travel--at least accurate for its time. While other 1950s movies had their rockets zooming to Venus or Mars without a care for time elapsed, fuel, or other matters of basic physics, the fundamental science of space travel is critical to this movie's plot.
When the rocket lands on our nearest astronomical neighbor, the astronauts realize they don't have enough fuel for the trip home. They try to lighten their load but conclude that they have to leave one person behind. Other, finer points of space travel are there as well: the depiction of acceleration, the need for air locks when entering and exiting the ship, and more. The rocket uses a nuclear engine, a technology that was under serious investigation for a long time (and may yet see its day in space).
Interestingly, the movie's premise is that private industry would build the first rockets to the moon, with the government leasing them for use. That's not too far off from NASA's current plans. While it's not the most riveting movie, Destination Moon was a big departure from the giant insect movies and tales of alien rocket ships that followed it for years. And again, like 2001, it had a towering science fiction writer as its adviser: Robert Heinlein, one of the fathers of modern sci-fi.