Update.
I’m so embarrased… I forgot to mention that when I left home (a few minutes after the landlord had driven away from the house) I noticed a brand new mailbox. I thought “maybe he came to replace the mailbox, and then decided to snoop around the house, or maybe use the bathroom.” He may have even rang the bell, but since I’m hard of hearing I may not have heard it when taking a shower. In any case, nothing justifies his entering the house (whether he’s incontinent or not!).

The event took place on a Monday. That evening, when commenting all this with my wife, she said that maybe I had left the door unlocked. Impossible, I said, as I’m obsessive-compulsive about locking doors and windows. Then we remembered that my brother-in-law had visited us the day before (Sunday) and that he had let himself out of the house. I’m not 100% certain that my BIL left the door unlocked, but is a real possibility.

So…

(1) My bro-in-law visit could explain the unlocked doors (he’s not very bright… I was working on another room when he left, and my wife didn’t walk him to the door because she had to take a phone call).

(2) The shiny new mailbox explains what the landlord was doing outside the house on Monday.

But something fishy still remains to be explained: when I left the house at noon that day, the new mailbox was not firmly fastened, as if the landlord (or whoever intalled it) didn’t quite finish and had to leave in a hurry. However, when I came back home that night, the mailbox was firmly fastened and all the screws looked tight.