All the costumes seen at the Criminology Museum were fully functional, meaning they could all indeed be worn. The plaques accompanying them also included trivia on the specific costume based on the original cartoon.
At one point in the film, Scooby and Shaggy are pretending to sing into a toilet brush "microphone". The song they are actually singing is Strangers in the Night - Frank Sinatra's version featured the improvised scat lyrics, "Scoo-bee-doo-bee-doo", lyrics which then-CBS executive Fred Silverman chose as the name of the new cartoon series. The original name for the dog was "Too Much", a popular catchphrase of the era.
The original Scooby-Doo episode dealing with the pterodactyl ghost featured a villain and motive that were quite different. The pterodactyl/hang glider costume was used to smuggle pirated music, with the small-town mayor behind the whole scheme.
The trivia items below may give away important plot points.
This film for the most part makes absolutely no references to the previous Scooby-Doo (2002) film, however, at the end of the film when Shaggy is asked to wear the helmet, you can hear Scooby say "Mary-Jane is a man in a mask" to some fans, a line from the first film. The second thing to a reference is a picture of Fred from the first film, seen in the old clubhouse.
There was a gag, created by the animators at Rhythm & Hues, where Scooby would turn into his cartoon version when he mistakenly drinks a potion. The gag was not in the script and was at one point chosen to replace a less-favored gag in which Scooby would turn into George W. Bush. In the end, Warner Brothers decided that they didn't want the audience to compare 2D Scooby to 3D Scooby, so they chose to have him turn into the Tasmanian Devil instead.
When in Wickles mansion, the Gang finds a Celtic book with names written on the first page. Among the names are Harry Hausen (a nod to Ray Harryhausen, pioneer of stop-motion animation monsters), Werner Brovas (Warner Brothers), and Munster Mash (The Munsters (1964) plus the novelty song Monster Mash).
The Cotton Candy Glob is a tribute to the Cotton Candy Monsters who appeared in the story "Goop on the Loose" in the Scooby-Doo comics published by DC Comics, where the culprits were a child and two henchmen trying to get revenge from being fired from a carnival. The Cotton Candy Monsters were mentioned in A Pup Named Scooby-Doo: Terror, Thy Name Is Zombo (1989).
The metal slide rule which Velma uses to calculate how to negate the effects of randamonium is, in fact, an E6-B flight calculator. The E6-B is an incredibly important tool for pilots to calculate wind velocities, air and ground speeds, fuel consumption, time en route, and aircraft course headings, among other things.