Mick Jagger owned an original four-rotor Enigma encoding machine which he loaned to the film for historical accuracy in constructing props.
Kate Winslet was pregnant with her daughter during the filming of this movie, so the schedule was arranged around that, and at the end of the movie when her character is pregnant, she didn't need a prosthetic.
When Hester Wallace decodes the long list of Polish names the camera zooms in on the name "Zygalski". Henryk Zygalski was a Polish mathematician who helped to break Enigma.
When he's tapping on the desk with a pencil, Tom is spelling out "Claire" in Morse code.