[adzii_nufc]

I've seen this but in later Battlefield games. It turned out to be the controllers if it wasn't a game breaking bug and the trigger thresholds for certain weapons. Rockets, snipers etc.

Rebind the fire button to the left trigger or a bumper. I can't remember if there ever was a trigger threshold setting in Bad Company.

If it isn't that problem, you're likely stuck with a game breaking bug. I remember you could shoot a tracer round with a tracer gun to lock onto vehicles in Bad Company but I can't remember that preventing a free shot.