Deliberate mistake: At the end of the movie Rocketman shows his lady friend a space blanket, out of which he states he made something: ballroom dancing outfits. The difference in the material is just too obvious for this not to be a deliberate mistake. The outfits aren't the slightest bit related to the foil they were supposed to be made of.
Deliberate mistake: During the "swirling onion ring" chair sequence, Randall is given a set of goggles that make his eyes "bug out", to enhance the comedic effect of the scene. In reality, these goggles are known as "beer goggles", because they intentionally blur and disorient one's vision. Various aeronautical and military entities use these goggles to simulate less than ideal visual conditions.