Complicated. Difficult. Expensive to prove. That's not the worse part. The dog owner most certainly needs legal advice -- in fact, needs legal representation. However, the losses and damages are not that great in terms of possible maximum recovery.
In some states, there is law that a dog is simply another piece of property, like a table or chair, thereby limiting the maximum judgment to the cost of further treatment, or the market value of the dog.
The point is that, after looking at the costs of getting these expert opinions, plus the cost of the attorney, the dog owner usually has to conclude that there is nothing that can be done except to politely ask the defendant vet to pay up, or go to small claims court with whatever you have and make the most forcible presentation you possibly can.
A very good analysis of the veterinarian malpractice issue: Terence J. Centner and Nikita Smeshko, Compensating Companion Animal Owners for Veterinary Malpractice Through an Alternative Dispute Resolution Mechanism, Journal of Social Sciences 7(4);597-604, 2011.