My songwriting partner and I do the backing vocals together, at the same time, on one mic. I've found that two people singing together into the same mic makes the backing vocals sound WAY more full and lush than just one person doing all the singing, or two people doing the singing on different mics. I've read the same thing from a bunch of pro producers. Two voices into the same mic almost creates a new voice that's unique. We start with the low harmonies that are easy to sing, and that helps us warm us up. They're not the most prominent backing vocals in the mix, so if they're not absolutely dazzling it doesn't matter anyway. If they're not in tune or really crappy, then we scrap them right off the bat and just redo them immediately. We listen as we go, and if something's not up to snuff, we throw it out. Doing several tracks irons out any pitchiness, and we usually do several tracks to get a big sound. At the very least four for each part, because we want at least two tracks of the same part in each stereo channel. That really fills out the sound.
After having warmed up doing the low backing vocals for every section that needs them, we're usually in good voice to do the main backing vocals in the middle register. And after we finish that, we're definitely warmed up enough to do the lead vocal. The backing vocals help in warming me up for the lead take, and the backing vocals themselves are usually satisfactory because we started with the easiest part for us to sing.