Despite what the night time shots showed over the Eiger, there was no full moon on or near the 18th July 1936. There was, however, a blue moon that month: the moon was full on both the 1st and the 31st July of that year.
In the opening scene one of the entries in Toni Kurz's Tourenbuch includes a blue stamp from the Neue Traunsteiner Hütte. The entry is from 1936 but this hut was built in 1938.
The newspaper "Berliner Zeitung" which Arau and Fellner work for was founded only nine years later (two weeks after WW II)
At the beginning of the film, when Luisa watches the news in the cinema theater, the voice-over gets the first-names of the alpinists who died on the Eiger wrong. It says Max Mehringer and Karl Sedlmayr, but it's the opposite: KARL Mehringer and MAX Sedlmayr. This may have been intended to show the unreliability of the report.