The launch

You calculated that out of curiosity? Wow! I'm impressed.

Heinlein served as the film's technical advisor so I'm sure this degree of accuracy is mainly due to his input. But the speed required to escape the Earth's gravity was actually known theoretically decades before, so Heinlein's contribution wasn't as remarkable as it may seem superficially.

As you know George Pal wanted the film to be as technically accurate as possible and to derive the drama from actual problems planning and making such a trip would present, instead of "artificial" or melodramatic conflicts or issues. In terms of scientific accuracy, most of the film was dead-on, and the mistakes that did occur were largely ones made in good faith, that is, based on what was believed at the time.

Even so, Pal (and Heinlein) did omit two critical aspects of a lunar launch that were theoretically well-established even in 1950, and instead went with depictions they knew at the time to be inaccurate. Pal said they did so because of the difficulties in adequately realizing the correct methods on screen.

First, they showed the rocket being launched straight to the Moon instead of first going into Earth orbit in order to gain additional velocity to boost them towards the Moon. Second, they made "Spaceship Luna" a single rocket that would make the trip to and from the Moon intact, even though they knew that a lunar (or even orbital) rocket would be staged, with portions of it being ejected as the flight progressed. (Heinlein even theorized that that portion of a rocket that landed on the Moon would likely in itself be "staged", detaching part of it from the return vehicle, as in fact did happen in the actual NASA flights.) In both instances Pal simply felt it would be too difficult and too involved to show the flight occurring this way, so he simply went for a more straightforward, if less accurate, depiction.

Ironically, Destination Moon's cinematic rival in 1950, the much less scientifically accurate Rocketship X-M, did have its rocket assume an orbit around Earth to gain velocity before heading off into space, and that rocket was a dual-stage one, with the first stage detaching from the main rocket just as they assumed Earth orbit. Odd that RXM should get two crucial details right where DM did not. Even the orbital speed and escape velocity mentioned in that film were basically correct.