Years ago -- maybe I should say decades ago -- when I was Secretary for A.R.M. we would receive an almost annual form letter from ASCAP wanting an agreement for music used at conferences / conventions. Well, we never had music performances at our meetings so these were not returned. But this does show to what extent the professional organizations will do to protect the members rights.

Well as a musician myself, just keep in mind that those copyright laws are just about the only way musicians can make even a couple of bucks any more. Gigs don't pay, no one wants to buy CDs, or downloads tunes for free. So at least with publishing and recording rights you might stand to make a handful of dollars.

Of course that does not apply to the handful of big names that get played 10,000 times daily on every radio station on the planet....

Again the music source was offered for personal use, and again you are using it commercially. If you want that, you have to pay extra license fees.

Or... you can make your own mix tapes, using recordings which
1) are in the public domain (e.g. OP),
2) the artist licenses openly for free for commercial use (e.g. "Podsafe"), or
3) you license from the artist directly and he gets 100% of the money, which I really like.
There are plenty of artists like that nowadays. There's no problem getting fully cleared music without dealing with the biggies.

You wouldn't buy real estate with title problems or easement problems. Don't use music with licensing problems.

My understanding of the music copyright law is that if you have a radio playing a local FM station, that is covered by the radio station's music license. However if you connect that radio to a PA system, it becomes a public performance and you need a license for your venue.

As I remember this was litigated over a storekeepr who had a radio playing near his cash register. His argument was that he was listening to the radio and he could not control people who might overhear his radio. The court bought this argument. This same argument covers radios playing in barber shops and similar locations.

My personal experience with ASCAP inspectors has been that they are very polite and not at all thugs. Perhaps there may be people who pretend to be ASCAP inspectors to shake down bar and restaurant owners.

You'll all be undoubtedly pleased to hear that such madness isn't exclusive to America!
We have a similar problem in Australia, although it doesn't always appear to be as zealously enforced as this thread may show.
I used to have a small fibreglass manufacturing business and usually had the radio on out in the workshop. One day, I received a letter from the Australian Performing Rights Association demanding that I pay a licence fee for broadcasting music in my shop.
My first reply was to point out that all I was doing was listening to the radio, but they insisted I was broadcasting, because it could be heard when someone walked into the shop.
My second reply was to tell them to get stuffed.
They then threatened legal action, so I invited them to see me in court. I didn't hear from them again.
At that time, APRA were having a blitz and as a music lover, I have some sympathy for musicians who never get properly compensated for their works. However, I felt this action was a step too far and was prepared to not yield to threats.
Cheers, Bob

ASCAP and BMI are both good and bad.

Good: they ingeniously package rights so they are simple. Imagine if they didn't exist, you played the radio on your station platform, and you would have to have a clerk write down every song played, and call all those artists yourself and send out 100 royalty checks for 3 cents each or whatever you negotiated. What a nightmare. ASCAP and BMI cleave this Gordian knot by charging you a FLAT RATE for ALL music they represent, and the rate is breathtakingly reasonable (per customer). To figure out how the money should be divided among their artists, they send staff out to randomly sample what is being played in various venues across America. It's imperfect and compromised, but uses way less accounting.

Bad: Their system STILL has a lot of overhead. They consume 13% of the money taken in. Even worse, they have mandatory minimum charges of over $600/year combined. Even if your proper, per-customer royalty is $13. The whole system is rigged to make costs prohibitive for small and ultra-small outfits. No wonder the little guys ignore the law. They would happily pay the artist (label, really) the $13, they just don't want to pay $600 for the privilege, lol! ASCAP and BMI need to do something about that. Until they do, it's easier for folks like us to get off their crazy train and deal with independent artists directly, or the public domain.

Edited to make the language more clear.

LET'S MAKE THINGS MORE DIFFICULT
If the license for the music says "free for non-commercial usage" are we covered since railroad museums are mostly non-profit?

It's not more difficult, you just don't understand what "commercial" is. Railroad museums are commercial. Their nonprofit status only holds back the government. Private parties don't have to do you any favors because of it.

That said, if the songwriter and performer said "free for noncommercial use", good chance they would say yes to nonprofit use, for free or a reasonable rate. Drop 'em an email and ask nicely. and remember to send them a donation letter for their taxes.

Also, several companies are working to provide solutions. Here's your fully licensed station platform music, for $300/year, fully licensed, cleared and wrapped up in a bow. Half the cost of an ASCAP/BMI license. http://www.dmx.com/pandora/