Alternate Charlie Francis grows a full head of hair in the interlude between Seasons 2 and 3, but only three days were said to have taken place.
At the start, Olivia escapes her captors and has one of their guns. She is seen running towards the river and jumps in. At this point she does not have the gun. She is in a hospital gown and there is nowhere to hide it. She is then seen getting into a taxi with the gun.
While driving away from the shoot-out at the petrol station, the taxi's back right window goes from open to closed to open between shots.
The pistol Olivia points at Lincoln at the gas station and the pistol she has at her mother's house, are two different weapons.
After the opening credits the scene begins in 'Over There' Manhattan. As always the name of the city is shown but it is spelled MANHATAN. This is because the scene is set in the alternate universe; the different spelling as Manhatan was established in Season 2.
When Marilyn Dunham first sees Olivia in her home in Tarrytown, it has been suggested that she calls out "Anna" - the name of the actress that plays Olivia, Anna Torv. However, a closer listen reveals that she actually says "Olive", the familiar contraction of her name that she was known by in her childhood.
When they realized that the experiment to transfer alternate Olivia's memory to our world Olivia, was successful, Brandon explained to Walter that alternate Olivia's "memory B-lymphocytes where carried across the blood-brain barrier and successfully transferred the memories". This is not possible as memory B-lymphocytes have nothing to do with memories as they are merely cells of the immune system that produce antibodies and are absolutely not related to neuronal cells. At best, one could imagine that a memory B-cell transplant might have protected our world Olivia against infection that alternate Olivia suffered earlier in life but certainly not transferred her memory.