The depiction of a dog spinning a wheel is quite accurate; the dogs were called wheel turners and were bred for that exact purpose, but became extinct during the late nineteenth century.
Both Danny Kaye and Cyril Ritchard played Captain Hook in different televised productions of Peter Pan.
This is the second Rankin-Bass special to star Danny Kaye, the first being "Here Comes Peter Cottontail" (1971).
Other episodes of "The Enchanted World of Danny Kaye" were planned (including Rip Van Winkle, Rumpelstiltskin, The Mikado, The Little Match Girl, and Punch & Judy), but never made it into production.