One of the more unusual questions we've received lately was from a bar owner in Michigan who makes live recordings of acoustic performances. One of his questions was about how to "dampen audience members" so their noises don't ruin the intimate recordings he makes.
Answer: Well, you start with some duct tape or a pistol and...
Seriously, about all you can do is try to use directional mics and keep them positioned in ways that reduce the amount of audience noise they pick up. Keeping them as close to the source material and as far from the audience as possible is the best way to accomplish this. Positioning a directional mic just half the distance from a source compared to what you normally do will make a huge difference (assuming this also moves it further away from the unwanted sounds).
This same inquisitor also inquired about working with the tracks later.
"When I do an acoustic songwriter, I point one mic up towards the singer's voice and another one down towards the 24th fret. I then usually have a DI from the guitar's preamp. I find that I get a really great guitar sound with a nice stereo spread. One technique I use in copying the Mic'd guitar track, inverting the phase, and panning one copy one way and the other copy the other with the DI guitar panned about 20% off center, but when I do this the vocal seems to get lost."
Two mics roughly equal distance from a source are going to pick it up equally. The direction they are pointed often doesn't have as much effect as you'd think. If you invert the polarity of one you are now mixing a signal back in that is canceling many of the frequencies, and this is what causes the voice to disappear. The effect works better on the guitar because the sound coming into the two mics from it is different enough that they don't just cancel out. Plus, you have the direct guitar track to maintain a strong, coherent presence. If you want to use this process to make the guitar sound better you are going to have to dedicate a mic to the singer. Even then, when you throw one of those other channels out of polarity it is going to alter the sound and presence of the vocal, but hopefully you'll be able to compensate with your main vocal track.