Do they show it wrong in movies, when they carry pistols on the belts muzzle facing down? Or was there some mechanism that prevent bullet falling out, that had to be disengaged before firing?
A muzzle loading pistol (or most other guns of the time) wasn't simply loaded with gunpowder and a bullet. Wadding made of paper, felt or other fibrous material was rammed into the barrel as well. This went between the gunpowder and the shot and on top of the shot itself. This served the dual purpose of stopping the shot falling out and creating a tighter seal to focus the force of the explosion.
So a typical load would be powder, wadding, shot and wadding again.
Edit: missed a word
Muzzle loading pistols relied on friction to hold the bullet in place. Customarily, the ball was of lead; which is malleable. The ball was wrapped in a cloth patch; usually greased but this was not totally necessary. It was pressed home against the powder charge with a ramrod. To dislodge the bullet from this location took a substantial about of force, and properly loaded, a muzzle loading pistol would not lose its ball not would any empty space develop. This was partly because under the pressure of the ramrod the bullet would deform somewhat.
Edit: There were also flintlock pistols that had no ramrod; they had a screwed on barrel that one would unscrew for loading. These had a very tight fit for the lead ball as well. The Queen Anne pistol pattern is one of those.