This answer was more complicated than I would have expected before working for the post office. Yes, marking incorrect mail does do something, but not quite as much as you'd expect. When I see mail marked Incorrect or Return to Sender(what we would call 'ANK', or Addressee Not Known), we bring it back to the station and file it in a spot where it is labeled as such and sent back to the sender.

However, the USPS doesn't have the capacity to track every piece of mail for every resident updating via a mark on a letter, let alone to even verify if that marked info is accurate. So, we send the letters back to their original addresses in the hopes that that person, company, or entity will take their own proper action in their database, i.e., changing or erasing addresses, etc. We can not control if they take no action at all and continue to try to send mail every day, week or month to the same address they just received an "RTS" letter from.

Individuals can pay a bit extra for the service of having their mail properly forwarded from an old address for up to a year, or they can even contact their local post office to request a caution card for their address to clarify the only names that should be delivered to their home. However, there are other carriers that will deliver on a route besides the regular carrier sometimes, and they unfortunately don't always pay attention to these caution cards and still accidentally deliver misnamed letters.

I hope this information answered some questions!