The biggest pest problem ( by FAR ) is possums -- the Australian variety , not the American ones .
Possums are a problem in Australia too ... we just aren't allowed to kill them
Although it is mostly just sleep deprived humans who suffer at the paws of the dreaded possum
We have one who lives next door, but goes out to play each night (sometime between 1am and 3am) gleefully bounding across our neighbour's tin carport roof before jumping into the tree just outside our bedroom window and running down through the branches and along the side of our house.