Earlier in the movie when the truck full of drugs was being taken by the two men who stole the starting mechanism, the driver's door is white. Later, when they are involved in the shootout with the two fake cops, the door is grey as it's being hit by bullets. Later when the truck is being refurbished, the grey door is removed and the white door is being put on.
When the two policemen approach the truck they stop their car in the middle of the road. At the end of the scene the police car is on the right side of the road.
When Malkina retrieves the user name and password to Westray's laptop from the blonde woman, she remarks that the password is "five digits", as shown on the hand written note. When Westray's laptop is stolen on the street, Malkina enters an eight character password.
Westray is reading a newspaper in a hotel lobby. When the Counselor sits down next to him, Westray tosses a fully-opened paper to the Counselor, but the paper is folded in the next shot just before the Counselor goes to pick it up.
When the Counselor is in his car, on the phone with the Cartel lawyer, his watch band changes directions multiple times.
When the Counselor is in Amsterdam, the diamond dealer tells him an Asscher cut diamond is a "modern version of the old mine cut." In fact, old mine cuts are early versions of round brilliants (and sometimes look like modern cushions). An Asscher, by contrast, is a step cut, sometimes called a square emerald cut.
Because a large portion of this movie is set in El Paso, Texas, you would expect to see automobiles with Texas, New Mexico and Arizona license plates on them. Many of the vehicles seen from the front have New Mexico plates attached to them. However, license plates are only installed on the rear of vehicles in New Mexico.
When Malkina says that she might go to live in Hong Kong, the other person retorts, "you don't speak the language". Due to long British rule, English is an official language there. Nobody in Hong Kong, who was likely to interest Malkina, would fail to know English well.
When "Wireman" Sam Spruell shakes the helmet to remove the biker's head the head comes out way to easily. For anyone who's ever put on or taken off a proper fitting motorcycle helmet you know how difficult it is even with leverage.
When the Counselor is in his car, on the phone with the Cartel lawyer, the mobile phone is upside down.
(at around 50 mins) When Malkina is driving the yellow Ferrari California on the golf course, the cables used for the internal cabin lights are clearly visible going through Reiner's passenger door.
When the sewage truck stops at the gate in Chicago (at about 1 hour, 49 min), you can see mountains in the background. There are no mountains in Chicago.