Brown Spots on Basil

I have a basil plant that is in a pot outside. The plant has started to get brown spots on the leaves. Some of the spots are small and some are large. It almost looks like the leaves have just turned dirty, but they're not. The plant has been doing well and really growing, I don't understand. The brown spots are under the leaves and on top. It does not seem to be on the stems. Could this be a fungus? I am watering on a regular basis but I am not overwatering. Please help me with this, I don't want to lose the plant.

The problem could be a fungus, bacterial rot or spider mites.
To avoid fungal or bacterial problems, do not get the leaves wet when you water and try to keep the plant out of drips or rain. A sulphur spray using flower of sulphur is a fairly benign remedy if keeping it dry does not work. For spider mites I would suggest Pyrethrum Soap spray (Catalogue #T2212) applied three times at eight hour intervals. Rinse the soil after spraying so that the soap does not make the soil too alkaline.
Are you sure that the plant did not get sunburn? When you move it outdoors from haing grown it in the house you have to do so gradually starting in shade and moving it over the course of two weeks into full sun.