Dutch's horse, The Count, is said to be an Albino Arabian Stallion. In real life, horses cannot carry true albinism due to Lethal White Syndrome. Albino horses are born with non-functioning colons and die within a few days of birth.
While Oleander Sage is poisonous in real life, its lethality is greatly exaggerated in game. In reality, it would take a fairly large quantity to kill an adult human. Here, its residue on an arrowhead can kill a grizzly bear.
Possibly deliberate: Before heading out, Dutch assumes the O'Driscolls are on the mountain to hunt them down, which Arthur denies and Dutch accuses him of doubting. However, when both characters encountered an O'Driscoll the night before, he said the gang was on the mountain to rob a train and didn't know the Van der Lindes were there. This may be deliberate as an early indication that Dutch hears and believes only what he wants.
When Arthur first meets Agent Milton, Milton claims he's "seconded to the United States Government". Milton's claim defies the law in 1899, as the Anti-Pinkerton Act was passed in 1893 which prevented the USA government from hiring agents of the agency.
When the Cattleman Revolver is being unloaded/reloaded, the hammer is seen being flush with the frame. This is incorrect, as the 1873 single action that the Cattleman is based on is only able to be fully unloaded/reloaded by cocking the hammer halfway.
One side mission involves Arthur helping an inventor named Andrew Bell, who claims to have invented the electric chair and requests his help in being able to try it out and get it sold. In reality, the electric chair had already been invented by Alfred P. Southwick in 1881, and the very first execution was carried out in 1890.
During the game it's mentioned there is a high bounty price on the van der Linde gang including on Arthur Morgan yet Arthur will still introduce himself by name to some of the strangers he meets.
Despite being wanted criminals the Van der Linde gang are never on wanted posters that are usually posted at Sheriff stations.
One of the things that drives the game's main story is that the gang needs to acquire enough money through various heists in order to escape from the U.S. government and live in Tahiti. However, when exploring and doing side missions, Arthur can acquire tens of thousands of dollars by himself, which could easily pay for everyone to flee without having to rob banks or trains.
If missions are played out of order, characters will make references to events that have not yet taken place. For example, if the player completes "Pouring Forth Oil IV" before "A Fisher of Men", Arthur will discuss the Pinkertons catching up with him, even if it has not happened yet.
When Sadie and Arthur are fighting off the O'Driscolls in "Sadie Adler - Widow", she yells at them that they killed her husband and burned down her farm. While the O'Driscolls did murder her husband, it was Micah who caused the farm to burn down. When he tried to grab Sadie, he ended up knocking over a lantern which set the whole place ablaze.
After being given his diagnosis in "Fork in the Road', Arthur walks down the street and dialogue that he's heard through the game starts playing. If you have high honor, you'll hear Hosea say, "if we don't stop soon, we'll all be dying." However, Arthur wasn't present when Hosea said this earlier in the game.
During a mission in Guarma, Dutch pays an old woman a bar of gold to lead he and Arthur through a cave. After the woman turns on them, Dutch kills her and then he and Arthur leave, without taking back the gold bar. Someone as obsessed with money as Dutch would not make this type of a mistake.
Captain Monroe's shoulder insignia shows the rank of 1st Lieutenant (single gold bar). A captain's insignia is two silver bars next to each other. Also a single gold bar was used for the rank of 1st Lieutenant until 1872, after that 1st Lieutenant was a single silver bar. The single gold bar wasn't being used at all in 1899, it wasn't used again until 1917 when it became the insignia for the rank of 2nd Lieutenant.