I would say you're watering too often. Only water when the soil starts to dry a little. Not bone dry, but less than moist. Watering every evening is not a good idea, as you can see.

Could watering too much really cause the leaves to get funky like that? Wild. Thanks for your help!

Could be the beginning if spider mites, but more likely depression from being kept indoors when all the other basils get to go outside. Basil does not like it inside, and leaves that form in bright light will suffer when deprived of their power source. Even in a sunny window, the plants are getting maybe 1/3 of the light they would get on "the other side". It really, really wants to go outside.

Looks like thrips to me.

http://www.google.ca/images?q=thrips%20basil&oe=utf-8&rls=org.mozilla:en-GB:official&client=firefox-a&um=1&ie=UTF-8&source=og&sa=N&hl=en&tab=wi

If you can't load that, go to google and type in 'thrips basil' and do an image search.

More info: http://www.hdc.org.uk/herbs/page.asp?id=7

Is there anyway that you could remove one of the affected leaves and take a good picture to send us? I think I see some patches of powdery mildew, but not really sure.