John Cleese was a big fan of the show and wrote much of the episode he appeared in, including the pirate sketch, his scene with Gonzo ("the ugly, disgusting one who catches cannonballs") and the finale.
In one of John Cleese's skits in which he plays a pirate, complete with a nagging parrot/possible wife. Shortly before the end of the skit, he asks, "Do you want to be an EX-parrot?" and fires off his gun, missing the parrot. This is a reference to the infamous Parrot Sketch from Cleese's Monty Python's Flying Circus (1969). Also during the sketch, Cleese says to Capt. Link Hogthrob, "Of course I'm a pirate! What did you think I was? A management consultant?" In real life, Cleese has his own company that produces management consulting films.
During the Pigs In Space sketch when the camera shifts right and zooms in to show Cleese and the parrot you can see on the bottom right a power distro component from the set of "Space 1999" (1975) with a "Moonbase Alpha" label. No surprise since Space 1999 had recently finished its two season run, was also produced by ITC in the UK, shot in the same studios and shared crew.