It looks like the IK constraints are being moved too far away from the leg bones.
This will give you a snapping motion.
http://imgur.com/l494n6y
If you want to prevent the feet from rotating you can disable rotation inheritance on the foot bones or parent them to a bone "before" the leg bones and use a transform constraint instead to lock their position at the tip of the lower leg.
I hope it helps! 🙂
