I know I've missed numerous episodes along the way but the gist I gleaned, so far, is that he has been hearing sounds from the upper floor of his house (in daytime) but wasn't able to work out where it was coming from.
He hired a medium/exorcist/tarot reader at one point. (!)
In the Wednesday episode he was buying new locks and a doorstep salesman made reference to recent dealings with a previous resident (a woman's name is mentioned). Heston looked puzzled so I guess it's meant to be implied that he's lived there for years and some imposter has been there. He warns the salesman to stay away and then closes all these locks and bolts as the episode ends.