Doctors, nurses, billing industry. What doesn't belong?

I love just about all the doctors, nurses, therapists, technicians, etc. I have come into contact with. It's kind of a shame, then that the medical billing industry is so very uncool.

Three incidents lately have reinforced this:

1. I paid a $277 bill related to my sleep study in June. I recently got a bill from the same company for $330. I did owe $54 for a new thing, but they ignored the $277 I paid.
2. I had some lab work done. They made copies of my insurance card and lab card. I was billed for the full amount because they said I didn't give my insurance info. A few days later Mom called, and they apologized and asked for my info. The very next day I received an Explanation of Benefits from my insurance company for the lab work that was filed before Mom even called in my info
3. I paid a $350 bill by online bill pay, and I paid it to the wrong company. This was all my fault; I filled in the wrong box on my list of billers. The wrong company, also a health care firm, took my money even though they saw it was not owed them, then when we called, agreed to return it "in a couple of months."

No. 1 is forgivable. The other two? Not so much.