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.
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.