William Powell v. Jack Lemmon
Lemmon gave a superb manic comedic performance as Pulver, but it was William Powell's smoothly comic and quietly dramatic delivery of Doc that should have been rewarded at the Oscars. The fact that Powell wasn't even nominated for this, his last screen performance, speaks volumes to ignorance of the Academy, as well as the BAFTAs, Golden Globes, and every other body that votes awards for film excellence.
Of course, Powell should have also won for My Man Godfrey back in '36.