When the three cowboys cross the Rio Grande, their left-to-right order on the screen is Cole, Blevins, Rawlins. Then when the camera returns to them a moment later, it is Blevins, Cole, Rawlins.
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.
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.
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." However, foreign aircraft may be registered in the US via a trust arrangement, provided the trustee is a US citizen or resident alien. Thus, Don Hector's plane could correctly display the US 'N' number.
The silver airplane in the movie is a 1952 Beech Model 18. The movie is set in 1949.
Just before the three cross the Rio Grande into Mexico, they pause on a ridge overlooking the river and it is flowing from from left to right. Nowhere along the Rio Grande, viewed from Texas, does the river flow from left to right. It flows right to left (southeast) into the Gulf of Mexico.