Corrected entry: When they go to the alternate universe (in part 1), they need Olivia (the one from this universe) to open a passage and the others to give her a boost, but when they come back, it's the alternate Olivia that is there, and in the first episode of the third season, they confirm that she doesn't have the ability to open a passage. So they should never have been able to come back with the wrong Olivia. So much of the show is based on "who" can travel between these alternate universes and "how", such a blatant mistake ruins it.
Correction: They came back to the "green-verse" with the power from William Bell. That's why Walter and William drove to Cambridge to get the machine from the old lab, they didn't think Olivia had the strength to do it on her own. That's why they were able to take back Faulivia with them. Without Bell they wouldn't have had the power for it to happen.
Correction: William Bell provides the energy this time and not alternate Olivia.