in the film 'hot fuzz' danny throws a shotgun to the ground and it fires and gets an old man in the foot

Depends on the shotgun....

Technically the only way that could happen, is if the trigger on the gun was set so light that a minor jar would set it off. Either that or something gets wedged in between the trigger and guard and sets it off that way . So it is a possibility but highly unlikely 1 in 100,00 chance