Visible crew/equipment: When the rocket lands on Zyra, at the end of the landing, you can see the wire at the nose of ship guiding it. (01:19:15)
Revealing mistake: During the first shot of the rocket ship coasting through space stars can be seen through it.
Factual error: When the messenger has given the photos and materials to the doctor, the data is given to 'DA' or differential analyzer (just like in earth vs the flying saucers). What is shown is a standard card sorter which does nothing but put cards in order. This machine then outputs its info to a standard plotter which can only produce x-y diagrams. It would be easier to do the verification calculations by hand using a slide rule and some graph paper.