The reason for the December date: a second-unit crew came back with shots of Phoenix streets that showed Christmas decorations. So the opening gives the date December 11, even though this conflicts somewhat with later talk about how hot it is in Phoenix that day.

December 11 was a Friday in 1959.
A continuity mistake: the date of the final scenes of Psycho should be December 20. In her first scene, Lila tells Sam that Marion left Phoenix "a week ago yesterday"; the plot climaxes the day after that, which would be Sunday the 20th. (The last plot day begins outside a church service.)