When Esposito is visiting the victim's home for the second time to go through the photographs, he asks Morales whether he would support the death penalty if Liliana's killer was apprehended. Morales answers; "He would just get an injection and go to sleep." Lethal injection has never been employed in Argentina and was legislated in Texas (the first jurisdiction to adopt the method) only in 1977, three years after the scene is set; hence, it is very unlikely that Morales would consider it as a hypothetical method of execution.
The perimeter advertising of Tomas Duco stadium (where the match is being held) is not from the 1970s. All the perimeter advertisements shown behind the goal line are from 2008, the year when the movie was shot.
The train station in the opening scene shows the bright yellow stripes on the edges of platforms for the people with visual disabilities. That feature wasn't used in the 1970s: they became mandatory a few decades later when the laws on barrier-free accessibility for the people with disabilities were enacted in many parts of the world.
The young Benjamín Esposito is left-handed - you can see it when he is writing some notes at the office, regarding Isidoro's letters. Old Esposito is, on the contrary, right-handed (check out the very beginning of the movie, when he's starting to write his essay).
In the scene where Irene and Benjamín are drinking coffee, her cup is empty. When she stirs it, you can see there is no coffee left in the spoon, yet she shakes it to drip the "pretended coffee". When she drinks, you can see the cup is empty.
We are to believe that Benjamin pulls on Irene's blouse, and pops off several buttons, but he didn't touch it, he missed. You can hear some buttons hit the ground, but none were actually missing from her shirt until the next shot.