We have one neighbour with two cats that are always crapping in my front garden. I tried some Cat Go Away powder from the Pound Shop which seemed to deter them for a couple of weeks. I just put a load of slug pellets down cause we've got a load of snails munching at my flowers so hopefully the cats will make a meal of them.
Our other neighbour had a rabbit that they left loose in the garden, one day last year it dug under the fence into our garden. We chased it back through the hole and went and told our neighbour who basically didn't give a sh!t. I filled the hole but 2 days later it dug under again in a different spot, I went out and blocked the hole trapping it in my garden then let it out the back gate and it was never seen again!