The medal Commandant Klein wears around his neck is an Iron Cross first class with oak leaves and swords. This medal, awarded for merits on the battle front, was only given if the recipient already had the second class iron cross, which is nowhere to be seen.
Klein (Dafoe) states that he is Untersturmführer but wears collar tabs of SS-Obersturmbannführer.
Commandant Klein identifies himself as Untersturmführer (second lieutenant) but
he wears collar tabs of Obersturmbannführer (lieutenant colonel).