Ok, I'll attempt an answer, based only on the movie (not the comics) and my small bit of knowledge about Norse mythology (paired with up-to-date Wiki-research).
First of all the movie depicts the gods as being just a kind of powerful aliens (wandering on the same paths as Stargate and it's farther-in-spirit Erich von Däniken already did), if I remember correctly. Indeed this isn't that bad an idea, as in Norse mythology (like in Greek mythology and I guess many other pantheistic religions) the gods aren't that almighty as the monotheistic gods. They can be killed by other gods, fight with each other, and aren't completely all-knowing by birth (I think Odin had to sacrifice his eye for gaining the power to see the future). They didn't even create the world on their own, I think. So they are indeed just another race of very powerful, maybe even immortal, but not allmighty, beings in the mythology.
Then Odin is indeed the highest of the Aesir (ases?, don't know), the higher of the two god races, so it makes sense for him to be the king of Asgard (the home of the Aesir) in the movie. Furthermore he is the father of Thor. But as said, he doesn't lose his eye in a battle against giants, as depicted in the movie, but sacrifices it in order to gain future-seeing powers.
But in mythology everybody knows Loki is the son of two giants (one of them being Laufey, as mentioned in the movie) and nobody would think he is Odin's son, I think. But even in mythology he is still counted to the Aesir and not to the giants, and is indeed somehow like a brother to Thor, with them getting into many adventures together (but also fighting each other when Thor is fed up with Loki's tricks). In mythology he is very ambivalent character, too. He is both intelligent and intrigant and often helps the other gods with his cunning, while other times trying to sabotage them and even fighting on the side of the giants and other monsters in the final apocalyptic battle. But he doesn't offensively try to kill all humans or even fight the other gods directly, as in the movie, though he would be best choice if the movie wants an intelligent and powerful enemy for Thor.
EDIT: It seems he is even banned from Asgard by Odin after he has gone too far with one of his intrigues and is actually the leader of the giants during Ragnarok (the final battle). This might be seen as parallel to the movie.
Thor is depicted not that inaccurately, I think, being very powerful and sometimes a bit carefree. He does more count on strength than on intelligence or tactics, but he's not dumb. But I think they made him a bit more likeable/friendly in the movie (/comic?) to better appeal to the audience. He also wields the hammer Mjölnir in mythology (though I'm not sure it has to be a hammer in all sources), whose feature to always return to Thor was also depicted in the movie. But he doesn't really have such a gang of co-fighters and friends as in the movie and I don't know in which way they are based on "real" gods (though one of them is called Sif, which is the name of Thor's wife).
The movie depicts the world Jötunheim to be the home of the Frost Giants, although they are actually from Niflheim (but this is just a minor deviation, as Jötunheim is the home of the Giants). But the giants and frost giants are indeed the main antagonists of the gods and Thor would often venture into their lands to beat them up, sometimes together with Loki.
The Bifröst is actually the rainbow bridge between Midgard and Asgard and is indeed guarded by Heimdall, so it makes sense, in the context of the movie, to turn it into some hyperspace teleporter or something the like. But it does just connect Midgard (say Earth) to Asgard and doesn't connect all the 9 worlds together, I think, as depicted in the movie (maybe they have to go over Midgard to reach the other worlds in the mythology?).
And this whole Destroyer thing (this guarding robot misused by Loki) is utter crap. And I think also this urn the giants want to steal doesn't have any real background.
EDIT: Regarding the Odinsleep from the comics, I don't think this has any real background. When in real life you say "someone is going to Odinsleep" means he is entering a very deep and long sleep. This goes back to a particular legend as part of the Sigurd-legend (I'm not sure how far this applies to the more modern and mythology-cleaned Nibelung-legend), where Odin made Brynhild sink into a very long sleep for doing something wrong (I think for killing or rather choosing the wrong men in her role as Valkyrie, at least in the versions where she is a Valkyrie). But I don't think there is any mythological instance of Odin himself going into a long and vulnerable sleep himself.
These were just some small and superficial things I could come up with. All in all I think they did quite a good job to transfer all those mythological things into some kind of "super-powerful aliens"-context and treated the mythological sources not that inaccurately, even if making some errors and creating some things anew (Ok, this robot destroyer thing was really rubbish). But besided that I was indeed surpised how they managed to turn a god into a superhero without hurting Norse mythology that badly (though an expert on the topic may think differently).