Corrected entry: When Douglas Hall first jacks into Los Angeles, he enters at about 12 noon. He even looks at his watch which reads 12:05 p.m. He then takes a short taxi ride to the bookstore, where he finds the 1937 version of Mr. Fuller. After talking to him for a couple of minutes, Mr. Fuller then looks at his watch and says "Oh, it's getting late. I would like to close up now." Obviously this was a weekday since Douglas started off working in a bank, so ~12:30 p.m. is late?
Corrected entry: The movie takes place in 1937 Los Angles. A billboard in the background of one scene is for Lucky Strike cigarettes, with the red circle trade mark. Before World War Two the circle was green.
Corrected entry: Maybe this one is nitpicking and I understand why it has been done, but anyway this is what I saw: When Whitney gets killed in the '30's the character he took over in the simulation gets transported to the "real" world. Given that the "real" world is a simulation too, and Douglas gets shot. In the real real world we should see the guy that took over Douglas with the "soul" of Douglas. But we get to see Douglas himself.