Some of the gauges/meters seen are for tape recorders (% wow and dB meters) and would have nothing to do with the navigation or operation of a spacecraft.
The main rocket executes several sharp turns in space using nothing but a tail burn. To change directions there must be some attitudinal jets that push laterally with respect to the rocket's axis.
Early on, when hero Ray Peterson (RIk Van Nutter) is doing his space walk to transfer from the ship to the station; some of the background stars blink is unison. First, they shouldn't blink at all, since there is no atmosphere in space. Second, even if there were variables or occluding binaries; highly improbable they would be synchronized.
At the moment the moon-ship crashes into Phobos, there is a cut to an explosion in which a parked car can be seen. This error is in my (cheap) "Alpha Video" DVD copy but does not seem to be in the version on YouTube.
When the space-taxi is approaching the Alpha II, the receding BZ-88 (as seen behind the taxi) much closer that the thousands of kilometers needed to be safe from the thermo-fields being generated by the Alpha II's photon drives.
When Lucy (Y13) is explaining to Ray Peterson (IZ41) why there are plants on the space-station, she says that the plants are for "changing hydrogen into breathable oxygen" (rather than releasing oxygen from CO2)