Problem as of 1.7.9. Since cats do not attack mobs, it is not only pointless for them to stand-up when attacked, it is also disruptive as pets often come between a mob and the player's sword every now and then and resulting in the player unintentionally killing his/her pets. This is particularly frustrating with respect to cats which do not do anything in combat and constitutes a disincentive to use pets.
I regularly encounter both issues: invisible lead and breaking lead (breaking much more often). Both problems occur when the chunk is unloaded and reloaded again. Still a problem as of 1.7.9.
This just happened to one of my donkeys. Donkey got pushed inside a wall, suffocated, and died. All the items inside the donkey's chest flew all over the place and I had no room to store them anywhere.