It is rare, but not unheard of, to find a perfect giveaway horse. Most have picked up a few problems along the way. Perhaps he scoots when you try to get on, maybe he bites when you tighten the girth, possibly he bucks. If you are thinking of adopting a horse, be sure and find out why he is being given away. Ask what he does well, then ask what he has problems with. If you are determined to take on a horse looking for a new home, it is a good idea to have your vet assess him: check eyes, mouth, heart, lungs, have your vet palpate the horse's back, tendons, suspensories, hoof test the feet. Any of these areas could be the source of a so-called behavior problem.
If there is nothing physically wrong, it may be a good idea to have a trainer assess and work with your new horse. Sometimes a giveaway horse is just sick of the job he has been doing and wants a change. Figure out what your new horse LIKES to do, then let him. Some horses are tired of ringwork; take them on the trail. Some trail horses flourish when asked to work in the structure of the ring. Sometimes a horse just doesn't want to be ridden--change that horse into a driving horse. Horses are very adaptable and wish to learn new things. They are happy when they have a job to do. The trick is figuring out what job they would choose, given their druthers!
If your horse is having a particular problem, email me. Perhaps I can help. I have been a horse owner most of my life, and an equine veterinary technician since 1980. I have seen alot of problem horses, and turns out, many had physical problems such as blindness, back soreness, stifle fixation, and other issues which led to some serious behavior problems. A painful horse is never a happy horse.
If I can't help with your problem, I can direct you to people who can. E-mail me at firstname.lastname@example.org
Highly recommended: http://www.gttrainingvt.com/