In the airport scene at the end, many of the troops are armed with M-14 and M-16 rifles (as indicated by the flash suppressors). Whilst these weapons would be contemporary with the filming, they are much later than the film's time frame (late 1950's).
Soldiers at the end are wearing fatigues consistent with the mid-1970's when the film was made, with subdued pin-on enlisted rank insignia on their collars (including a very visible Specialist 4th Class in the front), and subdued name and U.S. Army tapes (black lettering on olive drab fabric tape) above their breast pockets. In the 1950's, enlisted ranks were worn full size on their sleeves, unsubdued yellow on OD green (same as for their class-A green uniform), the U.S. Army tape above the left breast pocket would have been yellow on black fabric tape, and the name tape above the right breast pocket would have been black lettering on white fabric tape.
In a voice-over near the Montana - South Dakota border, Holly says "...at the very edge of the horizon we could make out the gas fires of the refinery at Missoula, while to the south we could see the lights of Cheyenne, a city bigger and grander than I'd ever seen." From anywhere along the border, Missoula would be over 600 miles to the west, and Cheyenne would be some 300 miles to the south; nothing short of a satellite view would allow you to see both at the same time.
When Kit records his confession on a record, he places coins in the machine and then flips the switch from 78 rpm to 45 rpm. The instructions above the switch clearly say "Before Inserting Coins Select Recording Speed." If he were following directions, he would have flipped the switch, then inserted the coins.
At the beginning of the movie, Kit meets Holly after a long day as a garbage man and his white t-shirt is spotless. Kit then asks Holly to take a walk with him, at which point the t-shirt is magically dirty!
Kit and Holly stand near the railway track and their shadows fall at right angles across the rails. Moments later, when he spins the bottle, their shadows fall (almost) in line with the track. See the shadow of the hut as Kit walks past it.
At the end, when Kit surrenders, he raises his hands straight up at first, but three seconds later they are slightly risen and bent over his head. After another two seconds, they are back to their initial position. During this sequence, the distance between him and the Cadillac changes as well.
Kit pulls into a gas station, asks the guy to fill the gas tank of the car, then pulls Holly's suitcase from the trunk. Between his arrival and his emptying the suitcase, the shadows have moved significantly. See the shadow on the green door of the (workshop?).