Raymond Burr did not receive an Oscar nomination for portraying Lars Thorwald in Rear Window.
In many ways this is an impersonal performance as we seem Thorwald only from a great distance from Jeff's apartment and we rarely hear him. When we do here Thorwald it is distance and faint. For the most part it is easy to argue that really all of the performances out the window are very much a product of Alfred Hitchcock the director and not as much by the actor. I would say that is possibly quite true for some if not most, but I would not say that really is that case as Thorwald who becomes the most interesting person out the window.
Thorwald of course becomes the most fascinating when Jeff suspects that Thorwald may have killed his wife. Before the suspicions we just see Thorwald which Burr does well as a tired and not particularly happily married man of his wife. There is nothing that one should expect really expect from him, as he may be just a normal unhappily married man. After suspicions arise though Jeff starts to look more closely, and more comes from Burr's performance as Thorwald. After the murder Burr does just right with his part as a man doing some sort of job, but the question is what he is doing.
Burr creates the mystery of Thorwald well suggesting something very dark about Thorwald, but still leaving it entirely open that Jeff just might have too much free time on his hand. This becomes less likely though as we see more of Thorwald, and more of Burr. In the close up moments Burr does his best to make the most out of them to actually create Thorwald into a villain that works well for the film and actually even a more in depth character than one would expect given the circumstances.
In his very short moments where we see his reactions to the accusations, Burr does not portray just a blunt one dimensional villain, but more effectively portrays a very scared man suggesting that perhaps Thorwald's murder was something quite sudden and hasty. This is not to say though that Burr does not make Thorwald a proper threat. In his face he conveys a certain instinctual violence that is properly freighting. It is not that Thorwald is exactly a serial killer, but Burr shows that he is certainly capable of murdering to protect himself.
My two favorite two moments of his performance sum up the success of his performance. The first moment being when Thorwald finally looks and sees that Jeff is watching him. Burr's look of contained anger, and fear is very chilling creating a great deal of dread as he leaves his apartment and goes to Jeff's. The second moments is finally when he confronts Jeff and Thorwald asks Jeff why he is doing this. Burr is terrific in this moment as Burr does not deliver the questions so much like threats but rather like pleads. In strange way Burr actually makes you feel a little sorry for him, becuase he actually manages to humanize Thorwald. He makes Thorwald honestly a character, but as well still a proper villain for the film.