After McMurphy hijacks the bus and is driving through town, there are some 1970s automobiles, including a Plymouth Duster and Chevy Nova, and a store with lots of color TVs in the window. The movie is set in 1963, according to the World Series broadcast.
While describing the imaginary World Series game, McMurphy has Sandy Koufax pitching for the Dodgers. However, the radio broadcast listened to by the orderlies in a prior scene identifies the day's contest as Game 2 of the Series, which Koufax did not pitch in.
When the doctors bring back Randle McMurphy from his treatment, they walk in, one doctor puts down his doctor bag, they lay Randle down, and as they walk out the doctor bag has disappeared and neither one is carrying it out.
During the fishing trip, when McMurphy comes out of the cabin we see Candy behind him wearing only panties and holding her shirt to her chest. After a two-second cutaway, we return to see Candy wearing the shirt. She could not have gotten dressed that quickly.
As the chief and the boys are being escorted through the doorway on the way to their ECT, the male orderly with Chief is not the same one as the one on the other side of the doorway. The second one is much taller, nearly equal in height to the Chief.
During the basketball game, McMurphy runs to the edge of the court, the camera follows and, for a moment, reveals an assortment of film production equipment including lighting stands, C-stands, lighting gels and even a crew member. Only visible in the wide screen version.
The Birmingham Church Bombing of 1963 happened in September and Hall, Cagle and Robert Chambliss were arrested September 30 but the World Series was playing October 2nd to 7th. That puts the scene with McMurphy listening to the news and watching the nurses being escorted by Turkle out of sequence.
Towards the end of the movie, there are multiple references to it being winter, the most obvious are: the television announcer mentions the "upcoming holiday season", and the morning after the party, a sign saying the date is December 11th can be briefly seen. However, in shots of the outside, there are leaves on the trees, birds outside, and other small details inconsistent with winter in Oregon.
After Billy is caught with Candy in the room, he runs out stark naked chasing after Nurse Ratched while pulling his pants up, then slipping on the floor landing on his right hip. As his bare butt is exposed, we can see a red mark on his right hip from previous takes before he falls on the floor.