When getting drinks at the first cantina they come to in Mexico, Blevins takes a sip of his drink from a glass. A few seconds later the girl is filling a glass and hands it to Blevins. He says appreciate it and starts drink his drink from the glass.
The Beech 18 airplane that Don Hector flies from his ranch to Mexico City every week has a US registration number beginning with "N." Aircraft registered in Mexico have registration numbers beginning with "XA," "XB" or "XC." The filmmaker seems to have been aware of this, since most shots of the airplane have the "N" on the fuselage partially blocked by a car or person.
At the end, when John Grady Cole is riding into Lacey's ranch, we first see him galloping across the field, with the two horses running free on either side of him. After the camera breaks and comes back to John talking to Lacey, both horses have bridles on and John is holding onto them.