Shih Tzu have become a popular small breed of dog and, as such, are now more familiar to 
small animal vets than in years past. They do, however, have some breed characteristics that are unusual for dogs in general that can cause (usually) unnecessary concern to a vet not familiar with the breed. This page repeats some of the points on the Breed Health page but groups together the most common things raised by vets about Shih Tzu.
Undershot Jaws
An undershot jaw (lower jaw protruding further than the top one) is a characteristic of this breed. Some Shih Tzu will have a level bite but an undershot jaw is mentioned in the breed standard. Their lips should be level but some will show their bottom teeth. This does not cause difficulty in eating except in rare, extreme cases. Poorly aligned teeth and missing incisors are common in many brachycephalic breeds.
Umbilical Hernias
Small umbilical hernias are common in the breed and are often caused during birth. A large hernia may require surgery but smaller ones will often close over naturally. Emergency surgery is rarely required but opting to have a hernia repaired during neutering can be a good option if it is still significant when the puppy is of an age to be neutered. Generally a small umbilical hernia would not be grounds on its own to avoid breeding a dog - unlike an inguinal hernia.
Pinched Nostrils
Shih Tzu puppies will often have pinched nostrils during teething. This problem is caused by the swelling associated with teething and almost always corrects itself once teething has finished, usually by around 6 months of age. The bubbly discharge from the puppy's nose is not serious if the discharge is clear and watery and the puppy is obviously thriving. If a puppy is obviously really struggling, is lethargic or showing signs of lack of oxygen then surgery may be required but this is a rare case indeed.
Reverse Sneezing
Reverse sneezing, or snorking, describes a condition in which the Shih Tzu seems to be unable to get its breath and begins to snort. It is most often caused by a slightly elongated soft palate that “sticks” until the dog takes a deep breath through its mouth. The most effective way to stop this is to put a finger over the dog’s nostrils, thereby forcing it to breathe through its mouth. Sometimes just a hug and some reassurance will do the trick! Unlike more serious problems found in brachycephalic (short-faced) dogs, reverse sneezing in Shih Tzu is quite common and is not life-threatening although can be very alarming the first time you experience it.