Talking with Nicol, Mark is incorrect when he says that Deja Thoris has a magic glove that "can zap anyone she doesn't like 15 million light-years in the future."
A light-year is a unit of distance, not time: It's the distance covered by the light in a year; but it is possible Mark doesn't know the difference.
The Nazis speak broken German with heavy English accents. This is understandable as their scenes are all reenactments with Mark (who presumably is not fluent in German) actually providing their dialogue.
Mark tells Nicol dolls cannot close their eyes. Yet there are some instances later on where Nicol has her eyes closed.
In many close shots on Mark Hogancamp's hands the hands are not those of Steve Carell.
There is a scene where Hogie uses NATO phonetic to spell a certain expletive ("Foxtrot Uniform Charlie Kilo!"). The NATO phonetic alphabet was not adopted until 1956, eleven years after the end of World War II. The correct phonetic Hogie should have used for the time period would have been "Fox Uncle Charlie King!" but as Mark's memory has been damaged he might have forgotten which version was in use at the time.