Yes, there ARE other tests.
You can do a blood test to see if your dog has low levels of thyroid hormone. This is a hereditary condition known to be recessive which means a dog can have normal thyroid function but still produce offspring that are hypothyroidism. Untreated hypothyroidism causes several serious side effects including agression, skin conditions, obesity, joint issues, and seizures.
You can x-ray hips to see if the dog has normal hip sockets but dogs can have normal hip sockets and still produce severe dysplasia. The best way to prevent hip dysplasia is to only breed dogs that come from families of OFA GOOD and EXCELLENTS which requires you to know the hip results of the parents and siblings.
You can have your dog's eyes checked by a veterinary opthamalogist who can detect changes in the eyes due to hereditary disease. Many diseases of the eyes are progressive and require yearly checks. Many of the diseases are recessive meaning that a dog can have normal eyes and still produce the disease. The only way to know the likelihood of their carrying the genes for the disease is to know the health status of the parents.