I used to be fastidious about writing "return to sender not at this address" on everything that arrived for previous residents or wrongly addressed, and putting it in a post box. For things that looked super important I would even call the sender.
I realised that generally the sender either doesn't care, or can't do anything about it. And in many cases, they've got alternative ways of contacting the intended recipient anyway. So now I only check the mail about once every few weeks (unless I'm expecting something) and put everything not for me straight in to file 13. Just as effective and less stress for me.