While the priest was in the Gestapo agent's office the agent pointed out a Russian religious icon, which he said he obtained in Moscow. The Nazis were very close to Moscow, but never were in that city.
Halfway through the film, Gebhardt appears wearing a combat tunic of the Waffen-SS, complete with the "SS" sig runes collar patch. The Gestapo, which was part of the Nazi Security Police, wore a modified version of the SS uniform to include a blank collar patch and green pipped police shoulder boards. This is the uniform Gebhardt should normally be wearing when not in civilian clothes.
While their fellow-prisoner is being crucified, the priests are singing the hymn "Pange, lingua, gloriosi" by Thomas Aquinas (1264). However, they are singing a German version of this song, which was not in use before 1969. In addition, even if they happened to know a German version, it would be more likely for them to sing the original Latin version, as there were priests from all over Europe imprisoned in this block.
Although the film takes place in January 1942, the bishop mentions the deportations of Dutch Jews, which began in July 1942.
In the opening scene where the priests in the concentration camp celebrate Mass secretly, the celebrating priest gives the others Communion saying "Corpus Christi", with the communicant answering "Amen". But this is how Communion is done in the new Roman Rite (Novus Ordo), introduced in 1969/70. In the old Roman Rite (Tridentine Rite), that was used generally at the time the story takes place, the priest makes the sign of the Cross with the host over the paten and then says: "Corpus Domini Nostri Iesu Christi custodiat animam tuam in vitam aeternam. Amen." ("The Body of Our Lord Jesus Christ may lead your soul to eternal life.") Then he administers Communion. The communicant remains silent.