Re: How do you slip the jab?
Slipping the jab, or any punch, is anything but a random accident and does not have anything to do with constantly moving your head. That is just wasted motion and that is how you get timed, because try as you might it is impossible to be random in moving your head. Plus, constantly moving the head will frequently leave you unable to punch, unless that movement comes from the feet.
To begin with, you should be out of range. Then you don't have to react to punches that can't reach you and you don't tip of anything to your opponent. The slip is a deliberate move executed to land a particular punch or to accomplish a particular thing. For example, if you want to get close while shortening your opponent's arms, you slip inside the jab and land the right hand to the heart. This is a natural slip and counter because the motion of slipping inside and the motion of throwing a straight right are the same; the target is wide open and you pull in close before he can get his left hand back and be able to throw the right.
It is important to make your slip sharp, like the motion when you punch, because it generally is. Again, mentioned above is the slip outside the jab, going to the right. That should be the same movement as throwing a left hook, which is why that slip (or parry) to the outside and the left hook counter is so effective against a guy that is really stepping with his jab.
You should never slip just to avoid a punch; stay the hell out of range if your aim is simply not to get hit. The only reason to slip a punch is to create an opening to land a punch so you should always practice the slip and the counter.