The inter-title dialog refers to rocket ship H23, yet the photo and subsequent references are to rocket ship H32
The rocket launch is boldly set for 2130 (9:30 PM) as announced by the smoke-writing plane. But the launch also coincides with the rising of a full moon. The full moon would rise much earlier, approximately 1800 (6:00 PM) local time.
Dr. Manfeldt's newspaper clipping contains the date "Donnerstag (Thursday) August 17, 1896". That day was actually a Monday.
Though many of the mistakes about space and the moon could be excused given our limited knowledge at the time this was filmed, the use of a fountain pen in space should have been known to not work. Fountain pens, or specifically the bladders of ink in them, tend to crack or leak everywhere even in regular air flight. This was known even in the 1920s.
When Helius listens for Friede's heartbeat, fearing that the launch may have killed her, we can see her breathing heavily.
When Helius is explaining the risks of high acceleration, the title card reads "...forty meters per second." - it should read "...forty meters per second squared." (as is shown on the gauge shown immediately after).