There are steel bushings in the bolt holes that are sort of like shims; they take up the slack between the compressor and the bracket. If you remove the compressor from the bracket, generally it helps to push the bushings back out carefully so that you don't have to fight the compressor back in. I use channel-locks opened wide and a socket over the bushing for it to go into, and gently "grip" the bushings through, being careful not to tweak the bracket; that aluminum will break!
Also, there are tabs in the front of the bracket that are meant to correspond to the single ground-off flat on each of the compressor bolts. This is why you should never attempt to turn the bolts from the front; only remove the nuts from the rear - if you turn the bolt head you'll break those tabs and possibly the whole bracket. I would check that the bolts are properly seated as I'm sure many people install them and don't realize they need to clock each bolt so that the one flat meets up with the tab allowing the bolt head to sit flush against the bracket.
If this keeps up you might suspect your belt tensioner, absolutely if it's not the original Gates style unit - if you have one of those cheapo aftermarket ones that the bolt sticks way out in the front from the body of the tensioner, those are notorious for letting the belt set up an oscillating-like motion and it sounds all the world like a bad A/C compressor. This can be proven if you VERY carefully pry against the tensioner just a little bit with something like a broom handle, to keep it from bouncing around, the noise should stop. Obviously if you're not super careful this can be extremely dangerous, do so at your own risk. Or just accept what I'm telling you; if you see the tensioner start bouncing around side to side crazily when the compressor kicks in, replace it with a real Gates piece.
Richard