While my bike (05 yz250) is running in gear with the clutch pulled in it will move slightly when I rev the engine. It makes a more noticable but still small jump if I start the bike in gear with the clutch pulled in. My friend's bike (also a yz250) does the same thing more or less.
So I guess I am asking, is this normal for bikes like mine or is it a common problem that can be fixed?
Its not uncommon for it to do this very slightly. Especially if the motor is cold. If it gets excessive I would tear it down and check to see if your clutch basket and inner hub have grooves. This will cause the clutch to grab excessively.