Factual error: The geographical context of the film is wrong. Riverton, Wyoming (as the name implies) is in a fertile agricultural river valley. The surrounding country is uncultivated desert. There is none of the extensive grasslands shown in the film. Moreover, even in the 1960s Riverton, which is a county seat and market center, was much more substantial than the film implies.
Continuity mistake: When Ennis brings Alma Jr. and Jennie to Alma at the Supermarket, Alma Jr. grabs a jar of peanuts off the end display. This causes a group of jars to come crashing down, breaking glass and causing peanuts and glass to fly all over. Alma squats down to the floor to help pick up the broken jars and peanuts, but when Alma bends back up and goes to bring the girls to the front of the store, all the jars that had crashed and broken on the end display shelf are now upright and whole before anyone had had the time to pick them all up.
Continuity mistake: In the second tent scene, just before Jack and Ennis kiss, Jack's left arm changes from being at his side in the first shot of Ennis (as Jack touches Ennis' face) to up around Ennis' neck in the second shot of Ennis (after we see Jack's face). Also, Ennis' left collar goes from flat to sticking up during the scene.
Other mistake: Jack Twist's Thanksgiving dinner has a TV clip from a 1977 American Football game which cuts to Ennis Del Mar's Thanksgiving dinner which has an ice skating competition from 1980 playing on the TV, but then later the charity dinner where Jack Twist meets his soon-to-be lover has a banner saying 1978, two years before the previous Thanksgiving scene with Ennis Del Mar.
Continuity mistake: During the final scene between the men on Brokeback, Heath's head is down, then up in a different view, then back down.
Continuity mistake: In the final scene with Jack and Ennis when they argue, Jack is holding his gloves in his right hand, then as he approaches Ennis at the truck the camera flicks to Ennis and then back to Jack, and Jack now has his gloves in his left hand. Although Jack's hands are out of frame for a short time, his arms/hands never come together and he couldn't possibly have switched his gloves from his right to his left hand in this time.
Continuity mistake: In the scene up on Brokeback, when they're talking about rodeo cowboys all being screw-ups, Jack jumps up fooling around and he's holding the whiskey bottle in his hand in the first two shots, in the next it's gone.
Continuity mistake: At the start of the scene, at the Charity Dinner dance in 1978, there is a couple on the dance floor where the female in a blue dress is being spun like a top across the middle of the dance floor at the front. Then in the very next frame, the couple are now arm in arm at the extreme right of the dance floor.
Visible crew/equipment: As Ennis leaves for his first fishing trip with Jack, Alma is holding Alma Jr, whose pajama shirt is lifted. Alma Jr's microphone wire is visible on her stomach.