Maybe going to the vet is an exciting thing for your dog since they usually don't go that often after they have had all of their shots and check ups when they are puppies. All the wierd smells and new people and other animals would be exciting. I know my dog always gets excited when we go to the vet because we don't go that often. I think this behaviour is pretty normal as long as your dog isn't getting aggresive. If you are really worried you could try socializing him more and getting him used to going out and seeing new people and places. Also, when you go to the vet try and keep your dog calm and when he is calm and not jumpy remember to reward him for his good behaviour so he knows that is how he is supposed to act
To have more control you could get him a body harness instead of using just the collar. With a collar if they pull they can choke themselves and with the harness it goes under their front legs so it takes the pressure off the neck and is easier to correct them if if they jump and keep them under control. You can get one at your local pet store. They come in differnt sizes and are not expensive; a large one is only $30. They are also great for training them to walk properly.