Sorry, but I gotta disagree with both of you. This is something I've understood from the very first time I saw the film.
To say that Jane has "absolutely no effect" is downright disrespectful to the writers. Jane (Along with Selvig and Darcy) were with Thor for his entire stay on Earth. The only thing that Thor did after finding out about Odin's "death" is drink with Selvig and then hang with Jane on the roof. Odin's death had almost nothing to do with it. The reason he becomes worthy again are directly connected to his relationship with humanity. There's a reason that the moment he gets his hammer back is when he sacrifices his life to save Jane and the other people of New Mexico.
I am being disrespectful to the writers by watching and understanding the film?
Lets start with this. Watch Thor. Ok, good. Now we can start.
How long do you think Thor is on Earth? According to you Jane kinda of flirting with Thor over a three day period has a more profound effect on him then the death of his father, a potential war between Asgard and Jotunheim, and his permanent banishment from the realm eternal. From his home.
But I'll give you a chance. What are these moments that show the profound effect that Jane has had on Thor? Where are the scenes that show her having a profound effect on him.... They don't exist.
When Thor approaches the hammer for the first time on Earth, he does so without having learned a thing. He is still acting exactly like he was before his father sent him to Earth to learn a thing or two. Thus he is unworthy. Then Loki shows up and tells Thor that he is responsible for their father's death. There is a clear change in Thor's demeanor and attitude the moment this happens. His voice becomes softer, his tone change, he suddenly becomes more introspective. He starts to finally consider how his actions effect others. Thor's actions have finally caught up to him and it causes him to reflect.
It is no coincidence that Thor starts to consider the feelings of others and treating others with more respect after he believes his father is dead. It isn't after meeting Jane or spending time with her. It is after he is told that his father is dead and that it is his fault. Why else do you think they emphasis that? Why does it come up again with the arrival of Sif and the Warriors Three?
When confronted the very next day by the Destroyer, what Thor does is finally embrace the lesson his father has been trying to teach him. That the actions of father, of a king, effect others. Their family and kingdom. When Thor, angered by the Frost Giant attack on the vault, walks into their kingdom and starts war, he does so without a thought of how it will effect the people of Asgard. That is why Odin sends Thor to Earth.
When Thor sacrifices himself to the Destroyer, it isn't about Earthlings, or Jane, after all he protects Sif and The Warriors Three as well. It is about protecting innocent people. It is about being a man, a father, a king. He knows he can stop it and he does.
And he does it again later, not protecting humans or even Asgardians. He saves the Frost Giants from extinction. Those that he wanted to destroy with his own bare hands.
This had nothing to do with Jane. This had nothing to do with a bit of flirting on the roof. You are applying classic character tropes to the female lead in this classic tale as opposed to observing what actually occurs in the film. The entire lesson Odin is teaching his son is no more crystallized then by Thor believing his irresponsible actions are the reason his father is dead. If anything, Thor has an effect on Jane and how she is.