I just started taking lessons again after not riding for about 6 and a half years. This is from my fourth/fifth lesson and my first time jumping in that long. Not the greatest shots/angles, but I'd love to hear what you think, good bad or otherwise.
I agree with the above. To elaborate - you're hands are posting along with you a little (I've seen worse - but it's still enough your horse is concerned).
What I see that you're going to want to fix is this: a little more bend in your elbow so your hands can follow the horse's mouth better. The extra bend will allow you a little more range of motion in order to do so. Also bending your elbows a little more will take up some of the slack in your reins. While you're at it - thumbs up! He'll be a lot less fussy when you get your contact firmed up and consistent.
Your heels are good, and just riding your leg muscles will become more and more effective - I can tell they're out of shape. If you get a chance, do a bunch of practice in your two-point to help firm them up. I do this as intervals with two-point in trot up the long sides, post in the corners and short side, and then 2 point again for several laps.
In the corners, focus on having him flexion in the right direction. He's currently pointing his nose to the outside around your corners, it should be more to the inside (but not a ton). This will come as you work on your straightness.