For some reason I could not see the cockpit view, nor any control surfaces moving in the entire film.
Still, I can see two things.
First, that was definitely PIO, not a natural tendency of the airframe. Tango explained that part well.
Also, the amount of nose wobble went beyond just roll induced yaw. Back in my twisty stick days, I had to put a reasonably large deadband into the rudder so that in the heat of battle, I wasn't unintentionally giving rudder inputs. Someone suggested that at every opportunity, I should release the stick. When I did so, the nose would invariably slew some back to neutral. That got better with the larger deadband and more practice. It (almost) went away completely with pedals. Remember, yaw-roll coupling works in both directions.
Now a little more on the stall characteristics of the P-40E. It definitely has a vicious accel stall, but it's low speed stall characteristics are relatively benign. It will give you a little wing wobble and buffet telling you that you have gone too far before it actually departs. Simply release a little back pressure on the stick, and everything is fine. If you have the stick planted in your belly, you will go from controlled flight into the beginning of stall, right through the buffet/wobble and straight into departure faster than you can pucker. Also, do not stand on the rudder to try to catch and hold the nose. That works for many AH aircraft, but the P-40 doesn't have the power to weight ratio to pull that off. When you are riding the stall, you MUST ease forward on the stick before adding any aileron or rudder, otherwise you leave your energy-maneuver envelope and get what Tango described. Once in the stall, the recovery is like any other aircraft. The only cure is airpeed over the wings. So, unload, unload, unload. The stick should be no farther back than neutral, and get off the ailerons and rudder. You can't just snatch the P-40 out of trouble like a spit or zero. You either have the altitude to recover, or you don't. And it does not matter what your opponent is doing, at that point your only enemies are Mean Mr. Gravity and Hard Mr. Ground. The sooner you unload, the better your chances become. Once you start getting some speed, you can ease in some control inputs to start to arrest whatever flavor of stall you happen to be in. In the P-40, that means eventually you will learn how to fly under trees to complete the recovery. Watch out for the squirrels.
When heavy on fuel, the already poor power to weight obviously gets worse. I used to fly the P-40 a lot, and 100% fuel was simply too difficult. I'm sure people with better skills can manage that heavy, and I used to practice at 100%, but I never even bothered trying to fight at 100%. At 50% fuel, the P-40 actually comes to life, and at 25% and a notch of flaps you can surprise the crap out of a bunch of people. So try 50% + DT and you get 100% fuel range if needed and a 50% fighting weight.
So in summary: larger rudder deadband, smoother on the controls, and less fuel. Good luck.