When sound sources that should be coming from the left or right come from the opposite side of your headset.

This is due to a flaw with the Xbox 360 wired controller. Either switch to a wireless controller to alleviate the problems or turn down your incoming voice level. To turn this down, hit the Guide Button > Personal Settings > Voice, and then turn the incoming volume down from 10 to at least 4 or 3. Afterwards, you can use the Mixamp to turn the voice volume higher.