In the beginning of the movie, when young Tristan gets clawed by the bear, the bear cuts him on his arm. But when his father comes to look at the wound, the cut is on his ribs.
Tristan writes Susanna in 1919 to tell her he isn't returning. The narrator then says many years pass. When Tristan returns he is told Susanna and Alfred have been married for several years. Tristan then marries Isabel who is 20. As Isabel was 13 in 1913/1914 it cannot be any later than 1920/1921, only a year or two after Tristan wrote to Susanna.
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 and his family meet Alfred and Susannah at the fair, Isabel hands the baby over to Susannah. In the next shot, the baby is back in Isabel's arms.
When Tristan is trying to break the wild black mare he captured, the amount of mud on his shirt changes from shot to shot after the horse throws him. The next morning when Tristan rides the now broken mare up to the badminton game, there is little evidence of any mud on his shirt, even dried.
When 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 US military protocol as he received these awards whilst serving in the Canadian Army and is not wearing them on a US uniform.
When Samuel is out on the reconnaissance (and before his death) a chlorine gas shell bursts behind him. Later, when Tristan is composing his letter home indicating that Alfred will be bringing home Samuel's heart his voice-over narration indicates a date in March 1915. The first German gas attack on the Western Front was in April 1915.
After reading the paper, Samuel stated that the British Army has been defeated at Armentieres and is trapped in the Belgian Lowlands. In actuality, the Germans did try to outflank the British Army, but were unsuccessful and the British retained control of that city and were never trapped.
At the end of the film One Stab's narrative says that Tristan died in the Moon of the Trees Popping which would be in the dead of winter. In the scene showing Tristan fighting the bear the leaves on the trees show that it is in the fall. Also, when the final shot freezes the bear is far too small to be real.
Isabelle writes to William in the spring (April time frame) 1913 that Samuel and Susannah are coming to visit Montana for the summer. The first evening at the ranch, Samuel mentions tensions between Austro-Hungary and Serbia, in reference to the prelude of the first world war. These events would have occurred one year later, in summer 1914.
Correction:
In February and October 1913, military action against Serbia was contemplated, but in both instances neither Italy nor Germany was willing to guarantee support. This would be reported in the US Newspapers.
Conflict between Austria-Hungary and Serbia had been ongoing since 1908 including the Balkan Wars (1912 - 1913).
During the war scenes, an "Air Ram" is visible (a pneumatic device for throwing a person up into the air, to simulate an explosion).
The language was incorrect for 1914-1920. The "F-word" was not in common use. Nor was the term "screw" as in "getting screwed" part of the vernacular in that period.
When Tristan is searching for Samuel, having been blinded by the gas, they are yelling each other's name back and forth. But the Germans with the machine gun don't even attempt to acknowledge Tristan coming up from behind them. Surely they would have heard him shouting and not let him run up behind them unchallenged.
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.
Shot is mirror image just after Alfred tells Tristan to marry Susannah.
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.
When Tristan goes on his scalping quest, he attacks two German soldiers who are lighting a cigarette at night behind their machine gun position, in full view of the enemy. No soldier in his right mind would have offered such a tempting target to an enemy sniper.
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.
When Tristan is hugging his father as he leaves for war, his coat reveals modern metal snaps that wouldn't have been available in 1914.
During the 1920's Susannah uses a nickel plated Smith & Wesson Model 36 revolver, but the Model 36 wasn't released until 1950.
Just as the animal/bear stage begins to takes over Tristan, he rides to Samuel's grave and as he leaves, an orange cone is visible. It's kicked up by Tristan's horse.