I'm a sucker for films that take place in the 1950s, even if I catch the occasional anachronism or just plain goof.
Unless really bad, they get points for trying.
Quiz Show - which I too haven't seen but once, but had thought about recently
Pleasantville - yes, even if it's more of a tongue-in-cheek TV-artifice
L.A. Confidential
Ed Wood
The Front
Last Exit to Brooklyn
Matinee - to stretch the 1950s just a year or two
Round Midnight
Far From Heaven