First of all, I know nothing. Nada, zilch, squat.
But I've received great advice about phase on another board, and I'll also share an observation or two.
Yes, checking in mono and listening for weird phase-iness are both good ways to go. Also, a main concern in this area is making sure that the low end remains full after bringing in each mic. IOW, when listening to each track separately, does the kick still kick after you bring in the rest of the mics?
One of the advantages of using a DAW is that you can actually SEE what's happening and where. You can also nudge (move0 each track in millisecond increments (or less/more, backwards or forwards in time), and you will really hear the effects of phase when you do this. That's what it comes down to in my mind. Are the waveforms grooving together or fighting eachother? If one wave is zigging and the wave from the same source on another mic/track is zagging, they might cancel eachother out, or change the tone.
You can even use phasing to your advantage. It will exaggerate or attenuate certain frequencies and can change the tone of whatever you're recording for better/worse.
Listen to a 'Phaser' effect unit. It's essentially emulating what happens when two signals move in and out of phase. When you move a microphone while tracking, what you're doing is changing the amount of time it takes for the sound of the source to hit the mic. We're talking teeny tiny increments of time here, obviously, that's why repositioning the mic by an inch will make a big difference.