The Farnsworth Paradox - S5-E10
Corrected entry: When everybody from both universes are going back to universe A they come out of the box in a different order then they went in.
The Farnsworth Paradox - S5-E10
Corrected entry: In "I Dated a Robot" the gang travel to the edge of the universe and see their parallel cowboy selves (which Farnsworth stated was the only parallel universe). In this episode, the box leads to a different (non-cowboy) universe where the outcome of flipping a coin is different. They then all go through many boxes each with many more parallel universes in them. David X Cohen mentions that this is a mistake on the commentary.
Correction: Even though David X Cohen has admitted it I fail to see the mistake. Up to discovering the various parallel universes in boxes, they thought that the cowboy universe was the only parallel universe. They were clearly surprised when they ended up in the parallel universe with the opposite coin flips, and since "I Dated a Robot" was produced and aired before "The Farnsworth Parabox" there is really no problem continuity-wise.
Correction: So time travel isn't a mistake, but rearranging yourselves inside of a box is? I'm pretty sure that, seeing as how they're changing universes, they could shuffle around their order and come out a different way than they went in.
Nick Bylsma