Many thanks, rdx, for posting that screencap of the wall calendar. As far as I know, you're the first person to spot it, so I think we should name it after you.
The screenplay dates this scene as 1966 but doesn't give it a month. However, the screenplay also describes the weather at the time as "windy, bitter cold" so placing it in January would be appropriate. (Jenny also has a runny nose). However, Ang's problem was that he wasn't filming this scene in Wyoming in the winter but in the Albertan Rockies in June - the scene was shot on June 9. However, he needed that exterior shot where Alma is taking in the laundry to establish the utter isolation of the cabin but, as it's June, the surrounding land doesn't look at all wintery. So I think he therefore needed the calendar to establish that this was supposed to be a winter scene, not a summer one, no matter what the surrounding countryside looked like.
The calendar certainly looks "authentic" to me but I've no ready explanation for lynx-eyed Lance's observation that on the calendar Tuesday is the first and that would be true of 1963 but not 1966. Maybe they had a '63 calendar available and not a '66, so simply replaced the heading with January, 1966. After all, that is all that is necessary to be known as no specific day is mentioned during the scene.
Isolating things like this I think is a way of honouring the meticulous care that went into the making of this magnificent movie. I think Ang and his screenwriters, Larry McMurtry and Diana Ossana, wanted events very much rooted in specific times and places and it is from this specificity that the larger themes emerge. One of these "specificities" is indeed time and its passage during the twenty years that Jack and Ennis have together. Ang starts the movie by indicating time in the most obvious manner as it says on the screen that it's Signal, 1963, but after that his approach is much more subtle. Of course, the children change with time as do Jack and Ennis in outward appearance. Even their voices change as they age. ( They were coached to have three different voices to cover the aging process). Then there are the more detailed references: dates on postcards, on banners at rodeos and dance halls, a date given by the announcer at the Fourth of July fireworks, appropriate film clips (Surf Party) or a TV series barely glimpsed in the background, changing makes of automobiles - more Jack, of course than Ennis - or bare statements like Lureen saying that Jack was only 39. Almost all of these can only be found in the movie and not the short story. I don't want to even suggest that this is "all" the movie is about but we do have a richly envisaged passage of time though which the movie flows and this, I think, it is proper to detail.