My 84 year old mom believes the neighbor has bugged her house, he's a creep and writes porn books which could be scaring her.

Gee, I thought the police would suggest a trip to the Geriatrician, the motion detector and other suggestions are good, you never know it is possible that the neighbour is playing games, but along with the other things, I think the trip to Geriatrician would be my suggestion, and most definitely to the lawyers.

As you have learned, you don't want to discuss your mother's mental state with her. You want someone to sleep over to gather evidence for the police. There is nothing wrong with her. Just ask her.

As she goes further into dementia, the "truth" becomes less important. Validate her perceptions as much as you can. Respond to her feelings, even if the facts are whacko. If you discover that she is hallucinating, tell her doctor, who may be able to medicate her.

If I understand the story about the MIL, she just forgot, and didn't remember doing it. She is covering her bad memory to save face.

You've got your hands full.

Dear Sue, Some of what you described sounds like what my 92 y/o uncle has been going through, especially when you mentioned tthat your Mom claims to hear voices through the wall plug. He has been claiming increasingly over a period of 6 months or so, that someone in his building was knocking on his door at night, ringing his bell, and calling him on the phone (which he didn't answer). His fears were not entirely unfounded, because, like your Mom, he had had some actual negative encounters with this person in the past, and has developed a fear of him. My uncle had recently been prescribed medication that he had not taken ever before, and since then, his hallucinations started increasing, and I started wondering if that might be the cause. Certainly he was starting to obsess over this person, and had been repeatedly calling the cops in the middle of the night to report the guy whom he cannot see or positively identify (he is legally blind). They were about ready to send social services over to evaluate his mental capacity, which appeared to be seriously in question lately, although he does not have dementia and is otherwise menatally sound. I talked about this with the cops and the building manager, and discussed the possiblility of installing a nanny cam outside his apt door, but the cops said not allowed unless we posted a sign announcing that visitors were under surveillance (which would defeat the whole purpose). Since I did not have POA at that point, a negative evaluation was something I hoped to avoid. I told him if he did not want somebody to declare him nuts and chance losing his apt., he better stop calling the police. I got him to agree to call me regardless of what time it was and assured him I would not mind the calls in the middle of the night. After about two weeks, I had had enough documentation. I decided to sleep over 2 nights in a row, just to see for myself what went on in the middle of the night. The first night, I basically stayed awake and absolutely nothing happened - my ears were pealed for the slightest noise. The second night, I did doze off and on, and my uncle actually woke me up shortly before dawn, having just come out of the bathroom, asking me if I heard the knocking and was I going to answer the door - he also smelled something like ether, which he claimed the guy was spraying around the cracks of the door (I had folded tissues around the edges of the door just in case he was right). Bottom line, nobody was knocking and there was nothing sprayed and nothing that smelled - the tissues were dry. I convinced him that he was just dreaming and led him back to his bed. The next day, I decided to run all of his Rx's throught the drug interaction checker online, and discovered that 2 of his meds had hallucinogenic side effects, and used in combination, compounded the effects. I then called his doctor to explain the situation and what I had learned, and asked him to double check the drugs and let me know what to do. The doctor decided to discontnue one of the meds, and after that, my uncle's hallucinogenic dreams subsided to virtually none.
Therefore, you might want to get your Mom's drugs checked out for interactions.
Something else I learned in my online research was that the elderly sometimes do experience hallucinatory dreams in the wee hours of the morning, especially just before dawn or just before waking up. The only other thing I have heard is that an undiagnosed urinary tract infection (UTI), even a mild one, could cause mental confusion and hallucinations in the elderly. I found it interesting the parallel scenarios we both experienced with our elders. I hope some of what I related is helpful to you. Please keep us posted with your findings to resolve this issue.