Continuity mistake: When the mermaid rescues Allen after the boating accident, the amount of sand on Allen's face changes from the whole side of his face to just his chin to hardly any sand at all. This goes on for the whole scene.
Factual error: When the TV store is closing at Bloomingdale's, The Richard Simmons Show is shown on the monitors. In 1984, when the film is set, this show was broadcast only in the morning and was not released in syndication. The show would therefore not have been playing on a television channel in New York City in the late evening.
Other mistake: When she breaks the TV's with her "voice" they pan to the salesmen. The glass display case is intact. Had her pitch actually been able to break glass the display case would have gone as well.
Other mistake: Joe Cirillo is credited as playing "Sergeant Munson", but his name badge in the movie reads "Edwards."