The film's appropriately-bizarre title for its Germany release was 'Daddy ist ein Kannibale', or 'Daddy is a Cannibal!'
The surname of the family in this movie is "Laemle", a likely nod to Carl Laemmle Jr., producer of such horror classics as Frankenstein (1931), Dracula (1931), The Mummy (1932) and The Invisible Man (1933).
The strange chemical herbicide that Michael's father develops to wipe out foreign jungles at his Toxico job is in fact real, although doesn't work by the same mechanism described in the film. Defoliants Agent Orange, Agent Purple and others were produced in the 20th century by Dow Chemical, and tested in an isolated Canadian military base town in the province of New Brunswick, then later used to wipe out jungles in the Vietnam War. The chemical contained dioxins and was extremely toxic, leading to birth defects and other issues in humans and animals, as well as damaging plant life. Parents was one of a number of satirical horror comedies to reference the Agent chemicals, alongside films such as Return of the Living Dead.
Shot in seven weeks.
Sandy Dennis' character "Millie Dew" is a play on the word "mildew", which means moldy, musty, or damp.