We are in the early process of adopting a 3-4 month old puppy from a rescue organization. The dog will see a vet who will hopefully do a point-in-time test for known conditions, but some conditions cannot yet be tested (Heartworm). I've heard sometimes newly adopted puppy becoming seriously ill right away. This is familiar to me since every cat I've rescued had a health condition for at least a month afterwards - usually a parasite.
What conditions might not be caught by the vet and what symptoms should I watch carefully for?