Revealing mistake: After Rygel realizes that he can loosen the soil with the dumped gruel, it cuts to John and Aeryn as they approach the Tavlek camp, and when Aeryn tells John, "I am going to take out every last Tavlek. No survivors. No mercy. Now give me the oculars," John holds up the syringe (with Zhaan's sleep mist) that Aeryn had given him earlier, and we can see "DG-4" engraved on the side of the gun, revealing that the prop dept used the model DG-4 aluminum air blow dust gun to play the part of the syringe.
Revealing mistake: When John and Aeryn are walking up to the safehouse you can see make-up mixed in with the rain dripping off John's nose.
Till the Blood Runs Clear - S1-E11
Revealing mistake: While John and Aeryn are in the module, which is leaking plasma, just as Pilot tells them that Moya does not want to put her baby at risk, we can see the puppeteer rods controlling Pilot's arms as they move.
Infinite Possibilities (2): Icarus Abides - S3-E15
Revealing mistake: When Crichton dies and Aeryn moves her hand to his face to close his eyes, he blinks.
Chosen answer: It's never explained. John mentions a theory that his less technologically developed craft simply interferes with the wormhole less than the "superior" Vipers, but they never make a concrete determination on that point. But we also have to take into account the fact that Moya traverses wormholes with no ill effect as well.
Garlonuss ★