Continuity mistake: When we see the professor's clone inside the tube there is a panel attached to a metal post going down to the bottom of the tube. When the professor hits the button to empty the tube of fluid it cuts to a close-up of the clone's feet and the metal post is suddenly gone.
New this week Factual error: When Professor Farnsworth visits the Bubbling Geezer to receive youthasizing treatment, the trained professional Heather says "botulism toxin tightens and tones facial muscles." Botulism is the actual poisoning, not the toxin. Botulinum toxin causes muscle paralysis which weakens the muscle, not tightening and toning of the muscles.
New this month Continuity mistake: As the power builds up in Bender, his left eye pops out, making him a cyclops, subsequently being eaten by the Cyclops eater. After the monster dies, Bender comes out, and has two eyes in the long shot, but puts his left eye back in the close up.
Continuity mistake: When Fry and Leela get to the moon landing site, Leela climbs in the moonlander hatch with the oxygen tank to which Fry's oxygen hose is connected. The hose is visible as it leads in to the hatch. When Leela pops her head out the hatch, the hose is suddenly gone. Then in the next shot, it's back, but lying underneath the hatch.