Is it inappropriate for my mailman to swear loudly as he's putting mail in my mailbox near my door?

Yes. I would have already called and reported him for the past problems and see if I could get another mail person to deliver the mail. I am sure that he just doesn't do it for just you, he has probably done the same thing with other people on his route.

Add: I'd be finding out who is over the post master at that post office and have everybody call them! That is outrageous and I'm trying to understand how he has managed to keep his route let alone his job.

No one's job is secure so don't feel intimidated to not pursue this up the management chain until this person has a clear understanding that inappropriate language as a government employee is unacceptable and either he learns to control himself or he'll be terminated. There is always someone there to replace you at work if you can't follow the outline of the job description. They are in and around private property and should ALWAYS TREAT IT WITH COMPLETE RESPECT.Tolerating it is how this country has completely lost its edge in the world. It's not ok.

Right after I got out of high school, I was a mailman for a short while. I frequently cursed a blue streak when there were "issues" on the route. Quietly, of course; really, I was muttering to myself, but I suppose people very close by might have been able to hear (but then I wouldn't have said anything if anyone was close by).

You shouldn't be able to hear your mailman cursing when you're inside your home. Call his supervisor and file a complaint.

Well, in his defense, I'm sure he didn't realize anyone could hear him, so he didn't know he was being inappropriate at the time. That said, he does sound like a bit of a fruit loop and should be reported to the post office. If he's about to "go postal" on someones butt, someone higher up needs to know he has anger problems on his route and could be a ticking time bomb.

"My mailman has been on this same route for over 15 years, and the post office will not change things. His job is secure" Then what on earth is the point of your question?

Honestly, if I heard my letter carrier swear like that I'd assume he stubbed his toe or cut his finger or accidentally dropped his mail bag in a puddle. "Son of a B...." wouldn't bother me one bit, but then again, I'm not a delicate snowflake.

Just let it go, for God's sake. So many problems in this world would be avoided if people just let things go. Who cares what this guy says to himself? He is there maybe 1 minute out of your day. What of it? You can't just dictate the lives of everyone around you. I understand not wanting things thrown in the bushes, but get a grip. And yes, it is probably inappropriate of him, and he is probably doing this to get back at you - but SO WHAT?! Let. It. Go.

Since this appears this isn't an isolated incident, he sounds like a total a hole.

If you are unhappy with your postal delivery man, then call the post office and complain. I would not be offended to hear the word "*****". He was probably not directing that phrase at you as people often get frustrated over on thing or another and say SOB.

Who cares??? Perhaps he's having a lousy day and just venting.

Of course that isn't appropriate. But he has a right to be angry, and to vent his frustrations.