He really seems to lack adjustability which probably stems from having very little correct, consistent flatwork. I don't have any huge issues with his jumping style. I think gymnastics would really help his rushing issues, but I also think he needs to be doing mostly dressage for a little while to help develop more control in all three gaits and to improve his rideability. If I got him, he'd be doing gymnastics twice a week, long hacks/hillwork twice a week, and dressage the other three days of the week. He's definitely got some talent, but he needs to chill out a little bit and relearn some things.
ETA: Also, he looks a little short on his right hind occasionally. If you're really interested in him, pay close attention to how he moves on a straight line and on a circle. Maybe it's just me, but maybe it's not.
"Always be yourself. Unless you can be a unicorn. Then, always be a unicorn."