Dogs can eat cooked pork. It is a prominent ingredient in many commercial dog foods, not very different from beef or chicken. The myth that dogs shouldn't eat pork may be related to the fact that raw pork can carry a parasite called trichinosis.
Raw pork can transmit trichinosis to dogs. Trichinosis parasites burrow into the muscles of the dog and can cause muscle pain and stiffness.
Others claim that pork can cause pancreatitis in dogs. However, the pancreatitis in these cases seems to be caused by feeding very high-fat table scraps to dogs that aren't normally fed table scraps, regardless of the pork content of the scraps. For example, some dogs develop pancreatitis after being fed high-fat turkey-based meals at Thanksgiving.