If you have been reading this board awhile, you will have seen Machiavelli refer many times to the lies that Amanda and Raffaele told. These lies are some of the evidence which Machiavelli relies on to be certain that they are guilty.
Well, Amanda told the policewoman the poop had been flushed. That turns out to have been wrong. It is seen as a lie Amanda made in an effort to control the investigation. The policewoman did not fall for it. The police found the poop and collected it - or at least a sample from the associated toilet paper.
Some Italians are very devoted to divining hidden meanings in the actions of others. They take it very seriously, and I have noticed that once they convince themselves that they discern a hidden meaning they don't want to change their view and recognize they were wrong. Italian has a word for it: "dietrology", which is roughly translated as "behind-ology". They look for meanings behind things. On this board our valued friend and contributor, Machiavelli, sees meanings and significance where the rest of us do not.
When Raffaele called police to report that someone had broken in through a window, the police operator asked him in anything was stolen. Raffaelle, who had looked in Filomena's room and had seen the broken window and rock on the floor, apparently also saw valuables in the room - a TV and laptop computer visible. He also had seen a camera on the kitchen counter or table. These valuables, the sort of things a burglar might take, we're still there. So Raffaele replied to the police operator's question whether anything was stolen that "No, nothing was stolen". Turns out that was incorrect (a lie), as cash, cell phones, keys, and credit cards were taken from another (still locked) room, Meredith's room.
The police and prosecutor and Machievelli cite this as a lie by Raffaele. How could he know if anything was stolen, they say. Proof that he attempted to steer or control the investigation.