Common Shih Tzu Health problems include the following:

Eye Problems

Shih Tzu have big protruding eyes that make them more vulnerable to eye problems than most other breeds.
They also have long hair that can irritate the eyes and you should try to keep all hair away from the eyes.
Specific eye conditions include:

Dry Eye

This is a condition where the tear glands do not produce enough tears, especially the watery part of the tear.
If there are no hairs irritating the eyes, but your Shih Tzu's eyes are permanently irritated, you should take him to the vet for a simple test to determine whether he has Dry Eye.
Take the condition seriously, as it can do serious damage to the cornea of the eye, and that can lead to eventual blindness.

Juvenile cataracts

It is a genetic condition mostly found in younger dogs and it can lead to blindness.
Dogs with this condition shouldn't be bred - so choose your breeder wisely.

Retinal Atrophy

Progressive Retinal Atrophy is also a gentic genetic which mainly affects older dogs.
It can also lead to eventual blindness. Good breeders have their dogs tested by a veterinary ophthalmologist to certify that they are disease free and you should ask the breeder for the certificate.

Cherry Eye

Cherry Eye will be visible as a large swollen lump on your Shih Tzu's eye.
Fortunately it looks worse than it actually is and your vet will be able to fix the condition by way of minor corrective surgery.
It is nothing more than a tear gland that comes loose and bulge out from under the eyelid.

Joint Problems

Hip dysplasia

It is a degenerative condition where the hip bone does not fit tightly into the socket.
This condition will be more visible as the dog ages and arthritis is not uncommon.

Slipping kneecap

This condition causes the kneecap to slip out of place causing discomfort to the dog.
The dog will often yelp and will not put any pressure on the leg.
The kneecap normally slips back into place when the dog stretches his leg, but corrective surgery is required in more serious cases.

Juvenile renal dysplasia

This is a serious condition that can eventually cause your Shih Tzu's death.
The dog is born with underdeveloped kidneys that never function properly.
This is a genetic disease and you should ask a breeder whether a genetic test was performed on the parents, as this condition is unfortunately very common in Shih Tzu.

If your puppy urinate excessively and has an excessive thirst, you should have him tested for this condition, especially if the urine is clear.
Your dog may also grow slowly, have no appetite and be very weak.

Dental Problems

Shih Tzu do not have a lot of space in the mouth and crooked or missing teeth are not uncommon.
Miniature Shih Tzu in particular suffer from problems with their teeth due to the limited space.
Other dental problems include gum disease and tooth decay.
It's best to brush your dog's teeth as part of the grooming routine, but as a minimum, have the teeth checked out by the vet at least once a year.
Small Greenies dental treats can also offer an easy way to maintian your dog's oral care.