Plot contrivance: At the end of the movie, Cogburn has to save Mattie Ross by bringing her to a city/hospital so that people can cure her hand that has been bitten by a rattle snake. Instead of taking a strong and rapid horse, Cogburn decides to ride on Mattie's pony. This is even more surprising when Cogburn actually rides the pony centimeters away from one of those strong horses and doesn't think about switching over.
Plot contrivance: When Chaney is hit on the head by Ranger Laboeuf, he is left unattended so that the Texas Ranger can try to save Cogburn by shooting from high ground. Both Mattie and Laboeuf are however surprised to see the villain Chaney stand up and attack them, even though he wasn't dead and that there was always a risk that he could stand up and kill them.