Corrected entry: Peter tells Olivia that the Greek phrase she said on waking up was "Na einai kalytero anthropo apo ton patera tou" and translates this as "Be a better man than your father." The Greek is grammatically incorrect (it should be "kalyteros anthropos...") and Peter's translation is wrong. The translation of Olivia's phrase is "May he be a better human being than his father." What Peter said is a translation of the Greek phrase "Na eisai kalyteros anthropos apo ton patera sou."
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.