(at around 1h 8 mins) The Jap guard's leg is grabbed by Pinhead, he falls to the ground and the top of his head is drilled into by Tunneler, showing blood all over his face at that time, next the camera jumps to a side view and the guy has no blood on his face.
The movie begins with "1939 Bodega Bay Inn", the entire movie takes place during World War II more than two years after 1939.
The overlay of the Bodega Bay Inn has black marks or blotches against the ocean waves.
(at around 19 mins) The USA Flag hanging on the wall in Danny's room has 50 stars on it. From February 14, 1912 through January 2, 1959 (which covers the time this movie took place) the USA only had 48 states so there would only have been 48 stars on it (1 for each state). It wasn't until August 21, 1959 when Hawaii became the 50th state that 50 stars appeared on the flag. The 4th of July after a state is admitted is when the star(s) are officially added.
(at around 1h 16 mins) The concentration camp Auschwitz is mentioned. This camp was build two years after the events depicted in this movie.
(at around 1h 14 mins) The female Japanese agent mentions Kamikaze attacks. No Kamikaze units existed until 1944.
(at around 13 mins) During the opening credits, you can see the marquee for a theatre. The film being shown is Comment tuer votre femme (1965). The film was released in 1965. Puppet Master: Axis of Evil is set during World War Two.
Beginning the movie, "1939 Bodega Bay Inn", Danny and Uncle Len converse and Danny wishes he was shipping out with the soldiers to fight "the japs or the krauts", among other references. This was two years before the U.S. entered the war.
(at around 1h 8 mins) The swastika on Max's armband is backwards.