Eh, he seems like he could be a nice enough horse with some better handling. He moves out okay for a western horse, though his head definitely needs some serious work. At the lope, she was constantly sawing on his mouth in a curb bit just to keep his head that low (hence why it was bobbing up and down constantly) and if APHA rules are anything like AQHA rules, then yes, his head is too low, especially at the trot.
I can't seem to get the APHA handbook to load on my computer but the AQHA clearly dictates that any horse who has his poll/ears carried below his withers, then it is an automatic DQ. If a horse is trained to lower his head on command but carry it nice and level, you can always just ask him to drop it lower if you need to. However, picking a horse back up after he's been taught to carry his nose in the dirt takes some doing.
This is quoted from the AQHA rule book regarding HUS horses:
The poll should be level with, or slightly above, the withers to allow proper impulsion behind. The head position should be slightly in front of, or on, the vertical.
Faults which will be cause for disqualification, except in novice amateur or novice youth, which shall be faults scored according to severity:
Head carried too low (such that poll is below the withers consistently)
Overflexing or straining neck in head carriage so the nose is carried behind the vertical consistently
So, that horse is nowhere near in accordance with the rules for a HUS horse. He'll need some serious re-training before he's competitive.