The biggest issue with poisoning operations is when the animals become bait shy, then it dramatically reduces kills, hence the popularity of warfarin for rodents - they don't associate the poisoning with ingesting the bait, so don't become bait shy.

I suspect in smarter social animals, bait shyness could be passed along as communal knowledge. In NZ we also use "pre-feeding" where the baits, without poison, are dropped for some time to teach the target species that they're good eating.

Predator by-kill can be a real issue though, and I guess it depends on whether the predators are pests also - like foxes and cats in Australia, mustelids in NZ. There's a reason NZ is the biggest user of 1080, there's no carnivorous mammals in our forests that we want to stay there, so if they eat a poisoned possum or rodent, bonus.

That said, Australia has carnivorous marsupials that are highly endangered, so it'll be a different ballgame over there.