Continuity mistake: In the early scene when Harry walks across the street to confront the wounded robber on the street ("Did he fire six shots or only five?"), the shotgun used by the robber is lying several feet from the robber's hand, but when he reaches the robber, the camera shot shows the shotgun just a few inches from the robber's left hand.
Continuity mistake: During the scene on the football pitch where Callahan is torturing Scorpio to force him to say where the kidnapped girl is, there are several shots as if from Callahan's viewpoint. As the camera switches between the two characters, the white painted lines on the pitch mysteriously move or even vanish underneath Scorpio.
Factual error: When Harry is confronting the bank robber and the robber says he has to know if Harry had any shots left, Harry cocks the hammer which rotates the cylinder. If you watch closely when he pulls the trigger the cylinder rotates again. This can happen only when the trigger is pulled in double action mode (hammer down).
Trivia: Dirty Harry's .44 Magnum was not the most powerful handgun in the world at the time. In fact, among firearms enthusiasts (such as screenwriter John Milius, an NRA Board Member), there were a few relatively-well-known examples of pistols that were more powerful. Perhaps best-known was that R.B. Rhodda & Co. of Calcutta had sold a number of side-by-side pistols in .303 British during the 1890's through the 1920's. The .303 is a relatively potent rifle caliber that is significantly more powerful than the .44 Magnum. With that said, I can certainly understand why an SFPD officer wouldn't be lugging around an unwieldy, side-by-side, two-shot pistol.
Harry Callahan: I know what you're thinking."Did he fire six shots or only five?" Well, to tell you the truth, in all this excitement I kind of lost track myself. But being as this is a .44 Magnum, the most powerful handgun in the world, and would blow your head clean off, you've got to ask yourself a question: Do I feel lucky? Well, do ya punk?