They don't actually 'skip' a generation but some conditions are recessive and dogs may inherit the faulty gene and pass it on without actually showing the symptoms themselves (they are known as carriers). And yes, to the question it is only the genes inherited from the immediate parents that are passed on, so no matter how inbred a dog is it will still only have what is passed on by its parents, even if their parents/grandparents etc had a problem. In some conditions (dominant) the gene only needs to be passed on from one parent for a dog to be affected.