There are several possibilities here:
1. Shooting while walking or running will be less accurate than shooting while standing, which will be less accurate than shooting while crouching, which will be less accurate than shooting while prone. Whenever possible, go prone.
2. The might be a symptom of FADE or an OFP bug. Read more about this here.
3. Maybe you really can't hit the side of a barn for your life.
Here's a little aiming cheat that some people use. The split moment you site or scope is on target, hold down the ALT key or the numeric keypad's asterisk ("*") key. This will switch you to mouse-look mode but your aiming position won't budge. Fire and remember to let go of the ALT key or press the asterisk key again to get out of mouse look mode.