Continuity mistake: When Shaggy and Scooby are performing the barber scene at the Coliseum, Shaggy is holding a sundial in his left hand and you can see that behind him there is a barber's chair, but when we see Shaggy holding the sundial in the next shot, the background has changed to a brick wall.
Continuity mistake: When Shaggy, Scooby and Scrappy have finished perming the lion's hair at the Coliseum, Scooby grabs Scrappy and sends the lion for a spin in his chair. In the next shot, the emperor says "Get off with the lion!" and he pulls a leaver releasing the trap door. But when we see saw the lion falling through the trap door, the barber's chair is nowhere to be seen.