When Joe picks up Julianna outside Canon City when they burn the corpse in the car to throw off The Marshal, both mirrors are on the truck, but when they drive back into town the driver-side mirror is missing.
When Frank withdraws the Colt from his coat, at the speech of the Crowned Prince, the hammer is already in the fully cocked position. When the little Japanese boy turns to look at Frank, the Colt is out and in the uncocked position. Frank's thumb is then pulling back on the hammer.
When Juliana and Joe turn over the film to the resistance you can hear the sounds of the bolts being pulled back on the Thompson Sub-machine Guns. This is correct as the Tommygun fires from an open bolt. However when viewed none of the Tommyguns have the bolt closed, therefore none of the guns could fire.
The photographers at the crown prince's speech use ancient view cameras or field cameras. Already by the mid-30s, Japanese companies that were to become Canon, Nikon, Pentax, Olympus, Minolta and others were successfully copying German 35mm photographic equipment the likes of Leica and Contax. Also medium format roll film. While it is conceivable that in the series' alternate universe, Japanese engineers might have felt less pressure for progress and further development after winning the war than they did in our actual universe with Japan losing the war, it is hard to conceive that their technology should have remained at a complete standstill for some 20 years.
Throughout the series "front line" troops still carry the bolt action rifles from WWII. Although there are some scenes of troops using MP-5s, G-36s, and Howa 64s. One would think that all troops would carry modern rifles not sub standard bolt action ones.