Frank uses eye drops to hide the redness in his eyes caused by alcoholism. According the DVD commentary by Sidney Lumet, this was Paul Newman's own idea.
Robert Redford was originally involved with this film. After writer David Mamet delivered his draft, Redford was uncomfortable with the main character and hired another writer to do another draft, and so on until Redford decided he didn't want to do the film. He was uncomfortable because he did not want to play an alcoholic. Sidney Lumet was offered the project. He read all the drafts and identified the original Mamet version as the one to make. At that point, Paul Newman agreed to star and received a Best Actor Oscar nomination for his performance.
After the verdict was announced in the film, director Sidney Lumet filmed two versions of the ending. In one version, the final shots seen are of Frank Galvin walking away from the courtroom in a series of long shots, never seeing what happens after he leaves the courthouse. In the version that was used, a sequence after he leaves the courthouse is seen.
Two cast members - Edward Binns and Jack Warden - played jurors #6 and #7, respectively, in 12 Angry Men (1957), which was likewise directed by Sidney Lumet.