The Korean War took place from June 5, 1950 to July 27, 1953. The time period of the movie "Cool Hand Luke" therefore could not have been in the late 1940's, approximately c1949 as indicated in IMDb Anachronisms.
Dog Boy fills Luke's plate with more food than Luke can eat, saying gleefully that Luke will be punished for not cleaning his plate by spending the night in the box. However, as punishment for his escape attempts, Luke is already being made to spend every night in the box.
Just before Luke enters the church to have his talk with God, he looks toward the church which is silhouetted against the late afternoon sky. In the next shot when he starts walking toward the church, it is dark.
During the fight scene with Dragline, Luke is knocked down into the dirt many times and is covered with black soil by the end. When the long shot shows Dragline walking away towards the barracks Luke has suddenly lost most of the black soil that was covering his sweat-soaked body.
When Carr gives his famous "Night in the box" speech, just after he tells Luke he hopes he won't be any trouble, he drops the spoons with a clattering sound. In that instant, the camera cuts from a close-up to a long shot, and the cigar stump clenched in his mouth is suddenly now in his left hand.
During the road tarring scene, the "boss" is walking in the midst of the crew shoveling sand in the close ups (he even gets sand on his shoes, which he inexplicably, doesn't punish), yet long view shots has him walking well, well behind the road crews' working area.
In the provocative roadside "carwash" scene, the blonde washes the car by rubbing her chest against the car windows and subsequently arouses the onlooking road crew (chain gang). In actuality the view as seen by the crew is obscured by the car itself.
The goof item below may give away important plot points.
Just before Luke is shot in the church window, a squib goes off so that Luke is bleeding before the bullet hits him. Also, the glass in the window is blown outward even though Luke is being shot from the outside.