We have two cats. They are kept in at night, encouraged out during the day. They do not come in for at least 2 hours before bedtime.
One (or both) keep shitting on the floor, in the bath, in their bed, on the stairs 
Yesterday my pregnant friend came round and used my toilet and went to dry her hands on a towel which had a fucking cat shit in it
I can only assume one of the kids picked it up off the floor and put it on top of the radiator. Mortified is not the word.
Tonight, I picked up my coat (which had been knocked on the floor) to find it covered in cat shit. 
I want to have a litter tray available to them permanently. DH thinks I am being unreasonable and he does not want a litter tray around for the youngest to get to instead they can just find random piles of shit round the house