What DJimC said. Actually the organizer/manager of the event or the owner of the bar/club is responsible that royalty fees are paid in most countries (and I think it is this way in the US).
I simply include in my contract always that I expect it this way and have never gotten into any trouble.
As for remixes: You are a DJ. You remix yourself a great deal of the time etc. Nobody (not even the music industry) expects a DJ to play a song through from A to B in its original form… kind of would defeat the whole concept of DJing and I had never a problem in any country with this matter.
The only thing you can get in trouble for of course is if you play stolen music (aka downloaded from illegal sites etc.) as the promoter/manager/organiser only pays the fee for you to play your music live (so the small print on CDs do not apply), but they still expect you to play legally purchased music and several times I had people from some organisation pop up and check my laptop etc. Although never in the US, happened mainly in Italy for some weird reason… but may be just pure luck hehe and they were usually friendly and nice after the first 2 mins they discovered all was OK and left me alone.
.
