Small time crooksters Nick and Charlie have an elaborate plan to rob an exclusive jewelers store. Using a variety of disguises and posing as rich old men and women they begin the set-up, but then Nick falls for the owner of a neighboring antique store and things get a little complicated.

When he accidentally takes possession of a top-secret invisibility potion while en route to his wedding, government bureaucrat Sam Cooper finds himself engulfed in a madcap free-for-all as Russians and other bad guys try to get the substance. To elude the Reds, his own State Department bosses and his livid fiancée, Cooper takes the vanishing juice himself—which only makes matters worse.