Tristan's bare upper left arm is shown in a scene which displays the distinctive dime sized scar of a smallpox inoculation. This scar is common to those of us (including Brad Pitt) living through the 1960s-'70s, but not for Tristan in the 1910s-20s.
In some shots, the log house used in the movie has a shiny modern metal roof, complete with snow-guards to slow the slide-off of snow. In other shots, or from other angles, the roof is comprised of rustic looking wooden boards.
During the night of the war, Samuel's cheek was scratched. The next morning him and Tristan were pulled down to a trench, still bearing the scratch on his cheek. Later on that day, he looks at Susannah's picture, without a wound on his cheek. Back at the camp, his scratch appears again.
When Tristan is preparing his horse to leave, after almost assaulting Susannah with his knife, he is shown tying a blanket to his saddle. As the shot changes from Tristan to Susannah's perspective, Tristan's hand positions switch constantly, from the top of the blanket to the bottom.
During infamous Tristan and Susannah's hug (after the boys announce they are going to the war), Tristan's lips move from Susannah's cheek to her forehead. Then camera angle changes, and his lips are again at her cheek's level.
After Samuel tells his father that he's going to fight in the war, there is a shot of him where Alfred's shoulder is barely visible behind him. When he runs to the stairs to talk to Susannah there is a closeup of him. Even though he has moved about five feet he is still in the same position as earlier in the closeup, and Alfred's shoulder is still visible.
When Samuel and Susannah are playing tennis early in the movie, as Tristan comes towards them on his horse the weather is clearly hazy. There is then a quick shot of Pet smoking a pipe which shows a perfectly clear blue midday sky. In the next shot of a visible sky showing Tristan with a windmill in the background, it's overcast or a completely different time of day again.
As the boys get ready to head for war, William Ludlow reads a letter sent to his wife. The letter notes the boys departed in October. Yet, the small deciduous trees visible still have leaves that are green. By mid-October in Montana, those leaves would have changed color and likely fallen off.
In the scene on the street where the two Ludlow families meet, Alfred is wearing medals for his service in the Great War. As he served with his brothers in the Canadian Forces from 1914-15 he should be eligible for three medals - 1914-1915 Star, British War Medal and the Victory Medal (1914-1918) - comprising one star and two discs. The medals he wears all appear to be discs and the colors of the ribbons do not appear to match the official colors of the medals named. Disc medals were awarded for bravery but only to enlisted men and as he was an officer he would not have received such. Note that in wearing such foreign decorations he is unlikely to have breached the Constitution as he received these awards whilst serving in the Canadian Army and is not wearing them on a US uniform.
In the final scene when Tristan fights the bear narration by One Stab says that Tristan died in the Moon When the Trees Pop. That would be late January or February. The leaves on the tree show it to be September or early October.
Right after Tristan's wife is killed by the stray bullet, Tristan is screaming on the ground. During this, you can see a lot of dental work (metal crowns) in Brad Pitt's mouth. This type of dental work would not be possible during the early 1900s.