In Lonesome Dove it is established that Call never called Maggie by her name, yet here he says, "Goodbye Maggie".
Wallace calls Kirker and Glanton Americans. At the time this film is set, Texas is still an independent republic. The scalp hunters are Texans, not Americans.
After the fight on the Brazos the Rangers approach the Comanche Call killed from down river. The body would have been carried down river from where the Rangers were fighting, not up.
When Shadrack picks the snapping turtle's head up you can clearly see it is made of rubber and is hollow.
When Augustus goes into Clara's store he hums "Oh, Susannah," which was written in 1848 in a scene that takes place in 1842.
The rifle that the scout, Bigfoot, uses is a Colt Model 1855 Revolving Rifle, which was not in use until 1855. As this film takes place in 1842 it should not exist yet.
Arrows shot by Buffalo Hump and other natives can be seen to be hollow aluminum arrows, especially at 29:24.
In this episode McCray is described as being originally from Tennessee and Call as being "pure Texan". In the original Lonesome Dove series, Call is described as immigrating from Scotland with his family when he was a baby.