When traveling back into the past, we see visuals from WWII, the Civil War, and Indians attacking a wagon train; these events are out of proper sequence. The Indian wars took place after the Civil War and should appear before it when traveling back through time.
If the researchers were truly monitoring past history on screen they would be watching scenes in full color, not the black-and-white of the stock footage the filmmakers used.
At 1:00:40, the diamond Stanton picks up off the ground is a cut diamond, not a diamond in it's natural uncut state.