Factual error: In the office motel of the Dallas Buyer's Club, a calendar behind Ron Woodroof's desk shows a newer model of a Lamborghini Aventador (2011-current) but the story takes place in 1985.
Factual error: The main character is wearing Ray Ban "P"-branded polarized sun glasses, which weren't available in the 80s when the movie is set.
Factual error: In the scene where Woodroof comes back through Mexico as a priest, the border agent asks for his passport. In the 80's American citizens weren't required to have a passport to visit Mexico, or asked to show one. That requirement began in 2009.
Factual error: In several scenes, characters are seen drinking from bottles of Shiner Bock beer (identifiable by the yellow labels) The bottles have modern labels (circa 2013), which are very different from Shiner labels in the mid-1980s, when the film is set. In particular, there is a scene in the motel where there are two bottles on the nightstand where the labels on the neck can be seen fairly.
Factual error: When Ron travels to Amsterdam you can see in the trunk of his car a Japanese magazine with the model Ai Shinozaki, who was born in 1992, but the story takes place in 1985.
Character mistake: When Jennifer Garner goes to see Raiana, she's wearing her white doctor's coat, which is ridiculous - doctor's never wear their white coats outside of the hospital; if they did, the coats would be contaminated with gas fumes, brushing up against garbage, all sorts of things could contaminate them, making them totally unclean.
Factual error: After getting the drugs in Japan Ron is packing a briefcase and you can see modern hundred dollar bills next to his passport.