Watch the episode where Dr Zoidberg is at his mating season, and watch the bit where they fight to the death. Dr. Zoidberg writes Dr. Z, and a little while later it disappears. Near the end of the fight, Dr. Z chops off Fry's arm, and Fry touches it and it is magically tied.
1st of all, Dr. Zoidberg DOES write "DR.Z" but he puts it on Fry's shirt during the Clawplah and he kind of tears it into his shirt. Secondly, Zoidberg temporarily reattaches Fry's arm on the ship claiming the operation a success.
This guy is right, Zoidberg does tear "Dr Z" Into Frys shirt, which disappears. And after Fry's arm is taken off I believe the author of this slipup means that Fry touches his shoulder and his shirt ties itself in a knot protecting (sort of) Frys wound. I can't tie a shirt sleeve together with one hand, can you?
These slip ups have always bothered me too, but lets be honest, this is a cartoon, it doesn't really matter.