HI lorrel,
If the dog has an inner ear problem such as an infection , this can cause vestibular disease which will give the dog a head tilt, and put him off balance. The constant shaking of the head can indicate an ear problem. In most cases this resolves after a few weeks but some dogs are left with a head tilt. The dog should have his ears looked at to see what is going on there. There are other causes of vestibular that are more serious such as middle ear cancer. I am going to direct you to a site that goes over possible causes and treatments. http://www.petplace.com/dogs/vestibular-disease-in-dogs/page1.aspx
The soft stool could be because in a rescue they rely on donations of food and some dogs have a hard time digesting a different food on a weekly basis. Keeping the dog on a regular diet may help with this. colitis, irritable bowel syndrome, bacterial infections, and malabsorption issues can also cause soft stool.
I would advise that before you bring the dog home you make sure he has gotten some type of health clearance so you are not stuck with large bills. Or make the suggestion of you having the dog looked at by a vet before you sign adoption papers. Rescues do feel a money crunch when it comes to taking care of multiple dogs and most do try to have the animals examined before they are adopted, but it is possible that as they stated they just haven't had the time.
It is definitely worth discussing all of your options when it comes to medical care before you adopt him.
dog training consultant
24 years training & behavior,pet first aide, Therapy dog eval., PA Animal Response Team
Hi Lorrel,
I was just looking up the Shepherd breed and it seems they are prone to pancreatic insufficiency which can also cause loose stool. You can read more on this here.
http://www.petplace.com/dogs/exocrine-pancreatic-insufficiency-in-dogs-epi/page1.aspx
German shepherd prone illnesses http://www.petplace.com/dogs/choosing-a-german-shepherd/page3.aspx