Goofs

Else tells her mom she is 18, and the law says she can do what she wants. In the 1880s, the age of consent was lower than 18.

Several of the wild mustangs have bridles. This can be seen clearly when the scene changes and the mustangs are running Right to left. However, it was stated when the group first spotted the herd that several of their own horses had integrated themselves into the mustang herd, and these horses would have had bridles.

The black mustang stallion they capture is shod (has horseshoes) which are visible during the chase.

At the sunset after Elsa kills the bison an aircraft's contrail is visible in the sky.

Elsa's mother says that she worked a sharecropper's farm and was pregnant with Elsa while James rotted in prison, but in "Behind Us, a Cliff" Elsa had stated that 18 years ago Lee had surrendered to Grant at Appomattox (1865) and that "a year later, I was born", making her birth date April 9, 1866. James was released from prison in 1865 (as earlier stated, he was imprisoned in 1862 after Antietam and spent 3 years in prison). She could not have been pregnant with Elsa in those 3 years. The only way her statement is even half-true is that she worked the farm 1863-1866, part of which he was in prison and part of which she was pregnant, but as a whole, her phrasing cannot be truthful.

Elsa says that she's 18, but in "Behind Us, a Cliff" (ep.2), she says that she was born "a year later" after Lee surrendered to Grant at Appomattox (1865), making the year of her birth 1866, and thus making her 17. Though given her rebellious nature, it's very possible she's rounding up to assert her independence in the moment, especially as she later admits she's 17.