All  dogs whether purebred or mixed, can have any number of disorders or diseases which are hereditary or are passed on genetically. Such conditions which are known to affect Bull Terriers include: 

-Certain heart abnormalities such as sub-aortic stenosis and / or mitral valve displasia 

-Hereditary nephritis (a kidney disease)

-Luxating patellae (knees) 

-Congenital deafness (deafness which the pup is born with, not that which may be acquired later) 

-Certain neurological disorders (like obsessive-compulsive"spinning", or the epilepsy-related "rage disorder") 

-Certain severe allergic skin conditions or other severe allergy-related problems. 

-Lethal acrodermatitis (a metabolic condition which inhibits the dog's ability to utilize zinc) 

However, though this is not a "complete" list, it does cover most common  conditions which tend to specifically effect Bull Terriers. 

The Bull Terrier Club of America, and health conscious breeders are very concerned about these potential problems, and are working to reduce the incidences of them. The BTCA recommends that all breeding dogs be evaluated before each breeding (or at least yearly, in the case of a stud dog) using the following tests / checks: 

-Veterinary checks for hereditary heart abnormalities, by the vet's listening for the "murmurs" which accompany these defects (there should be no detectable murmurs). Echocardiograms can also be utilized to detect any defects. We routinely have our animals checked by echocardiogram to be absolutely certain that there are no abnormalities.

-A urine protein-creatinine ratio test to detect hereditary nephritis (the result should be less than 0.5)  Based upon current information, we are now using a lowered level of less than 0.3 as a "passing" level. 

-Veterinary checks of the patellae, by manipulating the dogs knee area while applying moderate pressure to see if luxation or slippage occurs (there should be no luxation). 

-And, a BAER test for deafness.  The result for this should be bilateral normal hearing. We routinely BAER test our litters prior to placement since this test is accurate in pups as young as 5 weeks of age and need only be done once in the dogs life.

The other conditions mentioned would be readily observable. Dogs which display any neurological abnormalities as described above, and / or who display anything beyond a very mild allergic response should not be bred. As for those with lethal acrodermatitis, this is a congenital abnormality (affected pups would be born with it). Sadly, affected puppies have a very poor prognosis, and seldom live beyond a few very difficult months. Because of this, most are euthanized upon diagnosis of this condition.