FWIW, cats are fairly easy to break bad habits out of. A simple water pistol and a little time. Watch the cat and (in the letter box case) tempt it/them into misbehaviour with a letter (or gloved finger) through the slot then every time it/they show interest in the letter or finger, squirt them. Even water loving cats dislike being squirted! Won't take too long for the cat(s) to associate playing with things poking through the slot with being squirted and they'll stop.
Hide before you open fire though. You want the cat to associate the squirt with it's own behaviour, not you.
(This may also save you from painful revenge, usually meted out with sharp teeth and claws when your bare feet are sticking out of bed :arghh

now THATS satire
The only time I've been annoyed was when we had a holiday cover postie who decided to post the flat cardboard parcel with DO NOT BEND in huge big letters across both side, through a letter box it patently wasn't designed to fit through - yep, photographic prints, for a client - with a lovely fold about a 3rd of the way through them where he thought the message on the package wasn't for him and he could make it fit. I am aware that the contract is actually with the sender, so I took photographs, including one of it next to the 2cm's too small letterbox and mailed them to the lab, who sent another set promptly and dealt with it their end. No idea whether that would have got passed the 200 miles between offices though so that the postie responsible was made aware.