Like the other posters said, it depends on which herd you get them from. Both of mine came from the wyoming area and are both under 15 hands (14.2 and 14.3). There is another member on here with a mustang that is well over 15 hands. Big ones can be found, but you have to look a little harder. As for their jumping...... there is a reason why the BLM requires you to have 6 foot fencing before you can adopt. They can and will jump out over anything they can get their head over until they are tamed down some.
As for overall behavior and temperment, it's just like any other horse. Some are really mellow and others are really spirited, some travel smooth and others travel rough, depending on their conformation.
The only real possible health problem is that they are super easy keepers. Mine get fat on air and obesity itself causes problems in all horses. Other than that, I've not heard of any common health deficiencies.
All in all, with the proper training, they make nice little horses. I use mine for ranch work and they can work just as hard for twice as long as all the QHs we have.