It is not uncommon for the cord to be around the neck during delivery and the doctor then slipping it off. The cord can get a knot in it too but it is very rare for this to be so severe to cause a death or brain damage. This is just one of those things that someitmes happens and there is nothing you can do to prevent it. You often can't tell from ultrasound because by then the baby is large and you can't really see much of the cord anymore. This is why when there is a knot in the cord or it is around the neck, it usually isn't dicovered until delivery.
The fact that the baby moves a lot is a good sign. That tells you the baby is healthy. A healthy baby is an active baby. I wouldn't worry about it since it is so rare, you can't do anything about it anyways, and you have an active baby. If your baby suddenly becomes less active, then definately go see your doctor!