This problem is most apparent when placing microphones for a choir. But it can also cause problems in other instances.
The Problem With Too Many Mics...
You can experiment with this yourself by placing two microphones near each other and presenting a single audio source, ideally something with a single tone or even "white noise" (shhhhhhhhhhh).
As you move one of the microphones closer to or farther from the first microphone, you will hear a pronounced "warping" of the mixed audio content. This is because the same signal reaches two different microphones with a difference in timing and volume level.
The closer microphone receives a louder signal at a particular moment. The more distant microphone receives a quieter and slightly delayed signal than the closer microphone since it is farther away from the audio source.
Note: I'll link to a good video that demonstrates this issue below.
Where This Happens
The most common place this happens is with choir miking. It also happens when miking drums (especially overhead mics), overhead mics for strings, and vocal mics that are not held properly.
How To Fix It
When multiple overhead microphones are used to mike a choir or other audio source, you need to use a basic rule when placing them so that there is limited interference among the mics.
The basic formula for using multiple mics on the same source is the 3:1 rule.
Let's say Mic 1 is positioned 3' from the nearest choir member.
Mic 2 should then be placed 9' from the Mic 1 location.
Put in more mathematical terms, a second microphone should be placed three times the distance from the first microphone as the first microphone distance is from the sound source.
Yeah, I know, that sounds a little confusing. The following illustrations should help clarify this point.
Ultimately, you'll want to practice and experiment with your mic placement, and listen for what sounds best.
Just remember, as with most things sound related: less is more!
Use the least number of microphones on one source to get the best sound possible. That might only be one microphone. Or two. Maybe three or four for a choir. This goes for instruments too!
Just make sure to follow the 3:1 rule when placing multiple microphones.
And... Here is a good video that demonstrates the interference that happens when using two microphones on the same source.
Great Church Sound Learning Center.