Factual error: The bad guys attach over a pound of Semtex to the hull of the First Lady's yacht. When it explodes, the blast shatters the windows in a house a mile away, yet apparently doesn't impact the hull. Even as the vessel burns for 5 minutes, there is no discernible list.
Revealing mistake: At one point Charles Bronson wields a rocket launcher, the type which is a one shot disposable variety that comes pre-loaded with the rocket inside the launcher and it cannot be reloaded. The problem is, before he fires, he swings the launcher so the audience can plainly see there is nothing in the launcher just before he fires.
Factual error: When Killy slams the senator through the plate glass window to his death, the glass in the window is obviously not tempered safety glass, a requirement in glass elevators.
Plot hole: Senator Bunsen is introduced in the film as the President's Chief of Staff. As such, he would no longer be a sitting senator, and although he might be addressed as such, the newspaper lamenting his death would display his current title, not "Senator".