I don't think they meant that he is completely hopeless, just that at this time he definitely needs a lot of work :). I think he would go a lot better if you supported him more- this is especially apparent in your flatwork, where he is just going around on a loose rein. He isn't being asked to move out or use his back at all, and he isn't on the bit because he has no contact to accept. I think if you schooled him more on the flat with contact and asking him for a nice bend on a circle, he could really improve and be a great little mover. Put him on a 20m circle, get him on your outside rein by leg-yielding him out slightly, and ask him to rock back with a little half-halt. In your flat pictures, he is on the forehand and this definitely won't help with jumping! Once you elevate his forehand, I think he will have an easier time jumping.
Try to ride him more, rather than just sitting up there. I think that if you support him more, help him find his distances, help him stay balanced to and from the fence, he would improve lots. I would strongly advise gymnastics, just like maura said. Any horse can benefit from them, this horse in particular.
Your boy is so gorgeous, I think you've got a great little horse on your hands :). Good luck!