The film was at least nominated for Oscars for the Director, Writer (John Michael Hayes) and Cinematographer (Robert Burks), and also for sound recording (Loren Ryder). Not sound mixing you note, they didn't give awards for that then. They lost to Elia Kazan for On the Waterfront, which is in no way comparable to this, George Seaton for The Country Girl, which was in itself an adaptation of Clifford Odet's play, Milton Krasner for Three Coins in the Fountain, a lush widescreen film that is in no way as technically as good, and The Glenn Miller Story respectively.
As we saw in an accompanying documentary, Hitchcock on Sound, the director made careful and specific notes about exactly what and where his sounds were planted and shaped.
I personally would have thought James Stewart and Thelma Ritter should have been nominated - Stewart's performance, all reactions to things that probably weren't happening around him, is fantastic.