Otto Skorzeny is referred to as an SS Colonel. The four pips on his collar are the insignia of an SS Major.
In reality, Elek Cohen never posed as an SS officer. He posed as a member of the Arrow Cross and did save many Jews from certain death thanks to his disguise.
At various points in the film, baptismal certificates are shown, such as around 12:10 with a clear linguistic mismatch. On the top you see the words printed "Certificate of Baptism" and "Church of" in English, while everything else - both printed and handwritten - is in Hungarian.
Adolf Eichmann is shown to be wearing a Waffen-SS officer tunic complete with combat medals including the Knight's Cross with Oak Leaves which was an extremely high medal for valor. In reality, Eichmann was a security police colonel, typically wore a security uniform with bare collar tabs and green police pipping, and was never awarded a combat medal, much less the Knight's Cross.