Throughout the entire movie, Danker/Dussander's kitchen window is always closed. Except for the exact moment "Timmy" the orange cat needs to escape from being stuffed in the oven, then it's suddenly open. Magic cat anyone?
When Todd gives Danker(Dussander) the uniform, he is wearing a blue sweater over a red shirt. Minutes later when Danker comes down stairs wearing the uniform, Todd's sweater is missing and he's just in the red polo.
Mr. Kramer removes a "blood pressure cuff" from his arm to get out of the hospital bed. Blood pressure cuffs are not left on a patient, just used and then removed, so it should not have been on his arm.
Dussander is wearing glasses in the hospital as he falls asleep and Kramer goes and looks him in the face. Later, as he wakes up to find Weiskopf speaking in German, Weiskopf hands him his glasses. He then suddenly discovers Kramer's absence so it was obviously the first time he'd woken up since falling asleep with them on.
When Mr. Dussander opens the box containing the Nazi costume, he comments that it is a very good recreation and reads that it is from a costume shop in "Tappan, New Jersey". Tappan, however, is just over the border in New York state.
The SS uniform that Todd buys for Dussander has the collar insignia of an Obersturmbannführer (equivalent to Lieutenant Colonel). However the braided shoulder straps lack the single pips they should have for this rank.
Some question Dussander's description of carbon monoxide gas being introduced to gas chambers through pipes, pointing out that Nazi extermination camps used Zyklon B pellets dropped through openings in the roofs of the chambers, which then released prussic acid (hydrogen cyanide) gas. While the extermination camps, Auschwitz I, Auschwitz II-Birkenau, Majdanek and KZ camp Sachsenhausen and Dacau did use the Zyklon B method, most of the other major extermination camps (Belzec, Sobibor, and Treblinka II) and KZ camps used large gas or diesel engines to produce carbon monoxide exhaust, which was then routed to the gas chambers through pipes. This was learned from the experiences of the T-4 project. (The Chelmno camp had no gas chambers, it instead used gas vans, in which the vans' own carbon monoxide exhaust was routed to the rebuild and airtight cargo bay of the vans, which held the victims.)