Not formally checking out isn't the problem. Although, I highly recommend taking the minute or two to call the hotel operator/Front Desk and say you're leaving. The hotel can't clean a room they think it still occupied. If you've ever checked in early the day after a sold out night, it's probably because the hotel was able to clean your room early because that guest told someone the room was now empty.

The reason vacant but still checked-in rooms may cause this problem is because they typically get reported on lists. As Housekeeping finds these rooms, they typically create a list that gets delivered to the Front Desk. Sometimes, a staff member might make a mistake like transposing room numbers when creating or clearing those lists.

Hopefully I explained that better the second time.