Chiming in, I'm on a 200hz monitor and the gun is also not firing for me every time I pull the trigger. Upon first acquiring the gun, it only shot on the fourth shot. The gun still kicks back, but there is no audio, muzzle flash, or effect on the game world.
Edit: Just did more than 30 clicks in a row without a single shot. I like this game but I can't play it if it's gonna be like this.