In the final scene in which a man is shot in the airport (part of this scene actually recurs throughout the movie), the psychiatrist woman leans over him to hold him as he dies. From one angle, he reaches up to her face and his hand is clean. In the next angle, his hand is covered in blood as he touches her face.
The director chose Bruce Willis for the part for his ability to bring certain emotional themes into the diehard movie. He wanted that, but he also made a list of "Bruce Willis Cliches" he didn't want in the movie, including the "Iron Blue stare"