Dalmatians are relatively healthy and easy to keep dogs.
Like many other breeds, they can be prone to certain health issues specific to their breed. The primary health issues associated with a Dalmatian are Deafness, Allergies and Urinary Stones. And in that order of prevalence. Autoimmune Thyroiditis, Copper Storage Disease (CSD) and Juvenile Renal Failure is also showing up as potential breed problems.
Be sure to purchase your Dalmatian from a reputable breeder who guarantees your dog free of health problems and genetic defects. No one can be 100% certain that something won't ever happen to a dog from their breeding, however, they should be confident enough to stand behind their dogs. Should a genetic defect or inherited issue come up, reputable breeders may offer: a replacement puppy/dog (with or without return of the existing pet - owners choice to keep or not to keep), or a refund of a certain dollar amount of the purchase price. The latter is more common when selling a show dog, and the breeder refunds to pet price.
Breeders that truly are "preservationist breeders" and care about the future of the breed and the quality of puppies that they produce will try to ensure that each breeding is an attempt to "better the breed" as a whole. This includes ensuring their dogs are genetically good specimens, healthy, have excellent temperaments, and represent the AKC breed standard to the best of their knowledge prior to breeding. They should make health testing on their breeding line a priority.
Common health tests to be completed on a Dalmatian are: BAER (hearing), OFA or PennHIP (Hips and/or Elbows), CERF (eyes), and/or Thyroid. There are various other tests that may also be performed but these are considered the standard tests by many for a Dalmatian. A concentious breeder not only has the testing done but they try to turn the results in to the Orthopedic Foundation for Animals to be included in a breed-wide database. This way they are not only showing the health trends in their line, but also help determine the statistics for the Dalmatian breed as a whole.
Please note that just because a breeder has the health testing done does not necessarily mean that the dogs have all passed the tests with all normal results. Many times you will see bragging that health tests are all done, but make sure you check the status of the results! Why would a reputable breeder use a dog that does not have normal or passing results? Sometimes a dog possesses other good traits and the particular health issue is a minimal one or easily bred away from, so they may go ahead and use a dog that is not "perfect". We all know there are no perfect dogs. It takes a wise breeder with experience and a history of their line to include such dogs in their breeding programs. If they have otherwise healthy dogs and are not doubling up on the less than perfect trait, it is generally okay to do so. I always laugh when I think all that a reputable breeder goes through to pick a breeding and that humans would surely never procreate again if we had such high standards as those that we put on our dogs!