Surgery is not exact science. And unfortunately not every single one of them goes perfectly. There are risks involved. I assume (and hope) that you took him to a veterinary *specialist* for the hip surgery and not just your average community vet. If not, then a specialist is the first person you should see now because they may be able to repair the nerve damage...3 toes is not that bad. You need to understand that the doctor didn't do this on purpose, and your dog's life isn't ruined (dogs do VERY well with 3 legs), and unfortunately there anything that can be done to undo the damage. Now, having that said, the doctor that did the surgery is absolutely responsible for making things as right as possible. I would recommend writing a letter instead of calling for several reasons. #1. It will be easier to get your thoughts and arguements sorted out and stated in a reasonable manner. If you just call and start screaming at this person, you probably aren't going to get very far. After all, your whole purpose of confronting them is to get some sort of resolution. #2. You are more likely to get a letter to the boss than you are a phone call. #3. It leaves a "paper trail". A record that you have made an attempt to contact them and have the problem fixed... on the same note...be sure to keep a copy of what you send to them.
Next, I would recommend asking the vet that gave you the second opinion to give you some sort of documentation of their diagnosis. You may even want to get a 3rd opinion and get documentation of that as well. Mail in those documents with your letter to the surgeon. Keep copies of them as well. Make sure that you have some sort of solution in mind. What do you expect for the surgeon to do now? What do you want from them? A refund for the hip surgery? For them to pay for the treatment from here on out to treat the new problem (whether it be amputation or boot or physical therapy or whatever)? 20% discount off of annual vaccines for the rest of his life? You need to come up with a solution that would satisfy you and then make your requirements well known to the surgeon (in a letter of course).
Then, if the surgeon refuses to accomidate you, I would take it further. Do they work for someone else? If so, go to their boss. If not, contact the veterinary board or file a complaint with the better business bureau. You could even file a lawsuit if it came down to that. Don't let it go. They made a mistake and they should pay the consequences, but give them a chance to try to fix it first.
On another note...and 10 month old with hip dysplasia?? If you got him from a breeder, you may be entitled to some money back if the dog came with a health guarantee. It is a genetic disorder and any responsible breeder should have had the parents screened for it.
Lastly, I am very sorry for the situation that you and Boss are in. I wish you the best and hope that some physical therapy or other treatment may be able to save his leg. If not, I beg of you not to consider euthanasia. Three-legged dogs do just fine and live just a long, happy lives as their four-legged counterparts. I promise Boss wouldn't even miss it.