The gang calling themselves "The Scooby-Doo Detective Agency" is how Daphne, Shaggy, Scooby and Scrappy identified themselves in The New Scooby-Doo Mysteries.
The villain's face-within-a-face trick is like the aliens.
The female medium whom the gang suspects, but who turns out to be a real detective when she arrests the actual culprit, is named after famous New Age aficionado Shirley MacLaine. It's also worth noting that two years later, the character's name was recycled for a psychic valley girl–like white-feathered mallard whose friends refer to her as "Shirley the Loon."
After spending nearly half the episode banging on the basement door the kids barricaded, masked villain Boogedy Bones finally decides to go out the basement window, goes into the house through the front door, removes the random objects barricading the door and then goes back into the basement just so he can finally go through the basement door during the musical chase scene can be traced back to a scene from an episode of Bugs Bunny called "Buccaneer Bunny''." note It's when Bugs rows a boat, which is tied to shore and is propelled back but Bugs treads water anyway, to Pirate Sam's ship. Sam boards the boat but sees the oars on the ship stairs. So he swims out to the ship, retrieves the oars, swims back to the rowboat and rows his way to the ship.
"Now Museum, Now You Don't"
One of the items on display at the museum is an airplane called "Mahogany Pigeon" belonging to Harvard Huge, respective allusions to the "Spruce Goose" and its inventor, Howard Hughes.