When Nathan toasts Stingo on the bridge, as the shot pulls back you see first one then several cars from 1982, obviously an issue with how long they could hold up the bridge traffic for the shot, they needed to hold it up an extra minute or maybe lacked the budget to pay for late 40's cars to drive by instead.
In one of the early scenes when Stingo is moving in he is carrying 3 cases of Spam on his shoulder. They barely move despite him writhing around to get the door open. When he gets into the room he drops them on the bed and you can clearly see most of the cans are glued to the cardboard. The actor even flips the top row over on the bed and they stay attached.
When Stingo is packing to go back home and Sophie comes back home and is talking to him, you can see a pair of Nike speakers on the bed. Nike was established in 1964, much after the time when the movie is set.