The Palo Duro Canyon is roughly twenty miles south-southeast of present-day Amarillo. The canyon would be the location of the last significant confrontation between the Indians and the Army during the Red River War of 1874. Civil War veteran General "Three Fingers" McKenzie discovered a large encampment down in the canyon, including hundreds horses. Because of the difficulty getting down into the canyon, the Indians had plenty of time to cover a retreat, but they had to abandon the majority of the horses. Although McKenzie was not able to kill any Indians, he massacred some 700 horses. As an aside, it should be noted that the Palo Duro River was (and continue to be) not only a gathering site for wild game, but it is also a very rich source of red clay. To this day pottery shards are occasionally found there.
Cobb refers to the area as the "staked plains". This is a reference to the expedition of Francisco Coronado in 1541. Faced with an endless sea of grass and concerns about finding their way back, Coronado had his men plant a series of tall wooden stakes in the ground. In the decades that followed travelers would see the remnant of these stakes, which gave the region the name "Llano Estacado", or staked plains.
When Goodnight informs Cobb that they are near the Big Wichita River and not the Red River, this is not particularly serious. Given their proximity to the caprock, this would put them only sixty miles south of where they intended to be; setting them back by perhaps twelve hours.