Revealing mistake: In the scene where Jack Ryan uses the radio after the helicopter crash, the film is reversed - the word frequency appears as a mirror image.
Revealing mistake: In the scene where the president's motorcade is going to the stadium, it travels on overpasses, but there is other traffic passing below. These over / underpasses would have been temporarily shut down as well while the motorcade goes by.
Revealing mistake: At the end of the movie when Spinnaker is approaching Jack and Cathy, the wide shot shows the couple sitting further apart. When it jumps to the close view, she is much closer to Jack.
Answer: The song is the classic "Nessun dorma", composed by Puccini and sung (in this version) by Bruce Sledge.