Your hands are moving, the should be still. When you post, you throw your hips, it should be a little more natural and less obvious. Because you have a locked gripping knee, your lower calf swings. You have little or no bend at the elbow, or where you have a bend at the elbow it looks like you have piano hands.
Your hands are much more still, and you have a much better bend at the elbow. Your posting is much more relaxed, but I would like to see it improve even a bit more. You still push off your toes to post, causing a locked knee, and a swinging lower leg, but it is improved since the first video, to improve is a good thing.
When you post, try not to think about it too much (maybe because you were being taped?).. When you think too hard it becomes less consistant, you may have a couple nice posting moves, and then a really shallow one, then a forced one. Just let it come naturally.
Grip with your lower calf, not your knee. That will help relax your posting as well, since you won't be pushing yourself out of your seat with your feet (also why your leg swings), but with your abs and lower calf.
Post without stirrups, that will strengthen your seat and help you build lower calf muscle to grip with.
Your leg is swinging here also, grip with your lower calves, not your knees! You also pump with your upper body too much (which got better towards the end of the video). Your hands should be following the motion of the horse's neck at the canter. Your hands are either still or moving up and down, rather than back and forth. Both transitions were lovely, though. (From what I could tell on the downward transition, the jump standard was in the way lol)
Very nice flying changes! =] Your leg is still swinging, but again it is more subtle. You have a better bend at the elbows. Your seat is much better, and so are your hands. It looks like you pump with your body a little bit, but I think it is much improved.
I would like to see a more still upper body. You can move with the stride of the horse, but it should be subtle and not "pumping". I think the biggest way to improve this, is stirrupless work.
A little more movement of the hands at the canter, following the motion of the neck (although you have this down pretty well).. This is one of my struggles right now, I've always had very soft still hands until the past 4-5 months I never followed the motion of the horse's neck. You should be springy in the elbow, allowing for the motion of the horse's neck. Now I'm talking more to myself here, lol.
A stronger lower calf contact. This will help the swinging lower leg. Stirrupless work again, here.
So to answer your question, I think you've improved quite a bit! =]