The corner of Dunn's mouth is just a little bloody. The first lady is bloody after being assassinated. Woodward's nose and mouth are bloody after being hit by Dunn, and Braddock's head has a bloody cut after also being hit by Dunn. Dunn digs into a scar on Woodward's arm to pull out a computer key, but the scene is bloodless. Dunn has a small bloody bullet hole in his shoulder.
Several people are bloody after being shot at the end of the movie.
Obviously Woodward and those working for him have extreme cases of both as not only do they kill the First Lady, but they'll also kill anyone who knows anything about the crime, and they setup Dunn for the fall. Bickhart has been selling biotechnology secrets on the black market and is also involved in the First Lady's assassination. A government official turns out to be corrupt, just like the bad guys. In a Gulf War flashback, Dunn is ordered to shoot a courier who turns out to be a kid. His commander threatens to shoot him if he doesn't make the shot, so Dunn grabs him and they roll through the desert.