The movie presents January 4, 1983 as the date when the term AIDS was created in a proposition in the CDC, in Atlanta. The real meeting where the term was developed was July 27, 1982, and the reunion took place in Washington. (Source: Time Magazine)
The scene where Jim Curran inquires Don Francis about what's the butcher's bill mark on the board (the death toll revolving AIDS cases) in reality was something that in reality was an idea conceived by Selma Dritz, the character played by Lily Tomlin, as mentioned in Randy Shilts book.
The English subtitle translation of the French sequences contains errors. Most are minor, such as the English subtitles saying patients were afraid to come to a French hospital when the actual French said they were refusing to come, but in the first hospital scene, the doctor actually talks about "plaques" rather than "warts" as the subtitles indicated; plaques are the classic presentation of Kaposi's sarcoma.
The goof item below may give away important plot points.
Bill Kraus' final moments when he asks about his glasses (he was speaking in several European languages, no one understood what he was saying) happened with his friend Dennis Seeley (played by David Marshall Grant) and not with Don Francis, as the movie presents. (Source: Randy Shilts book).