Are you a Mexican citizen?  

Win-win.At any rate, if you have law students or med students or other grad students (preferably not theater or music majors - they're flaky party animals), see if there is an off-campus housing listing for their grad students, or go talk to them about how to advertise to their grad students.You have to be careful how you word advertising on Craigslist or anywhere, though.  

I had people calling me from bars with live music in the background, obviously inebriated, people who screamed obscenities at their kids while leaving me a message, on and on.  

Derek your neighbors can hear and feel your "thud thud thud rumble rumble" on top of their own music and through their earplugs and over and above an other ambient noise.

Also, is there a point where it's up to the tenants to solve their own problems and how do you draw that line--eg if there's noise or loud music in the neighborhood or other quality of life issues that don't apply to the physical integrity and function of the property.

Find any reason to turn away a music or theater major - drama!  

Consult an attorney and proceed with eviction and stop this musical roommate nonsense.

If a prospective tenant only has a Mexican ID but not a US driver's license, how do I conduct a background check?

When you go over the lease, provide them a tenant instruction sheet with your welcome packet that explains:- how they can pay rent- how to make a repair request- watering restrictions- how to operate unit's HVAC, thermostat, care of garbage disposal, location of main water shut off, gas shut off, breaker box- numbers or links to turn on/transfer utility accounts- how your city enforces noise ordinances and how this may effect those who violate it (BTW, your tenant  blasting his music so it can be heard at by other residents on the block  at 10 am is just as bad as if he is doing it at 4 in the morning). - anything else you feel tenant should knowOthers have given you some great suggestions for collecting rent automatically.

It's not fair and you'll have an argument on your hands.Noise - tell them they are expected to listen to music and movies and TV or whatever - with headphones.They must have their own phone.Laundry - have laundry rules if you have laundry facilities.Advertise for commuters, if you have a market for that - people who need a place to rent during the week for their job, but have a home they go to on weekends.Advertise for med or law students  - they are quiet and just want a quiet room where they can study.Another good roommate option is a fireman/woman.