The question is, what should the 'feel' of a goblin fortress be? Probably not anything really coordinated would be my guess. Goblins should take the chaos typical in poorly managed fortresses and turn it up to eleven. In short, goblins should be their own worst enemy. I think it would fit if they regularly had to deal with tantrum spirals, but had a way of surviving them.
Actually, Meph, you brought up that you wanted goblins to have several individual isolated 'towers'. The easiest way to encourage that would be to just work with the personality values they already have, which by default should lead to a lot of in-fighting. Splitting up your population should ensure that even if one group tantrums itself into oblivion, the others should still survive.
So going with that in mind, pets should probably be powerful (to make enemies easier to fight off) but also come with significant downsides just by having them around. Random, short-term outbursts, for instance, should create occasional deaths among the population, leading to potential tantrums.
They could carry contagious diseases, which should encourage the isolated-tower setup as well. This would also be a fun way of including diseases among the other races - goblin pets could roam wild in the caverns, and other races who tried to tame them would also have to deal with things like troll fever, jabberer flu and crundle itch. Oh, and rabies, of course.
Slaves require a lot of micromanagement. I don't think they'd work too well with the chaos that should be daily life in a goblin tower.