I watched it last night and thought it was excellent. I get very little post - all bills are paid by DD and I have internet billing, so no paper bills.
Most insurances are set up to automatically renew these days so very little paperwork there.
There is no post behind the door of the flat because it doesn't have a letter box. Mail is left on the table in the communal hall. If the baddie lives in one of the flats he (or she) can easily squirrel away any post that arrives for her. Or if he is clever, he would get it redirected.
Lack of dust - if the flat is tightly secured there would be very little dust. Most dust comes from human skin, clothing, day to day living, and insects.
Great drama with lots of questions, lots of suspects and great casting.