They look sunburnt. When you washed them off did you do it in the heat of the day when they were in full sun? Wet plants sunburn very easily. I would bet you didn't get rid of all the spider mites. Spider mites hatch out every 3 to 5 days and if you've missed 1 or 2 you'll soon have them back again.Spider mites are the reason I stopped growing impatiens from cuttings. I found I was fighting a losing battle.

Basil is very easy and fast to grow from seed. I'd burn what you have or dispose of dirt and all in the garbage and scour out the container. Then plant again. I'd plant the whole package of seed and then thin them when they get too crowded to whatever your container will hold. You can then use the small leaves off the ones you pulled in cooking.

Thanks so much! I was worried it was some sort of fungus. However, I have noticed that the spider mites have seemed to come back so I'll take your advice and start from seeds. Is there a good way to prevent them? I've read you can keep the soil very moist but then I'd worry about root rot.

fwl, no you mustn't keep the soil wet....that won't do anything but stress the plant. It is said that spider mites dislike high humidity and some people advocate misting the underside of the leaves and the plant in order to achieve that.

Spider mites like hot and dry and hate cool and wet. If you are growing them in a pot you might consider moving it to another spot. When you water--in early morning or early evening I hope-- wet the plant getting the undersides of the leaves. That might keep them away but I wouldn't guarantee it

Check the pictures in this article and see if your problem might be basil downy mildew. Unfortunately it is becoming more and more widespread every year.

http://awaytogarden.com/basil-pressure-fight-devastating-downy-mildew/