She doesn't look so much off to me as inconsistent and lacking connection in spots. If a horse is fighting contact, or changing it's frame like this, especially such a young horse, their step becomes inconsistent at times. But when she's going quietly and straight, or around corners she looks steady to me, not lame. If you're really worried about it, when you look at her bring a coach or someone knowledgeable with you, and do a vet check before purchasing.
As for height, a large stepping 16 hand horse is completely adequate to make the distances. I wouldn't worry about making the distances until the horse is under 15.2, or is shorter stepping. I have a 15.3 mare who often takes larger than 12 foot strides when she gets rolling. And remember Hickstead was only 16 hh!