zinnea leaves have brown spots,
Your plants may have bacterial leaf spot. The following is from our "What's wrong with my plant?" diagnostic tool. There is a link to a very good publication here as well. http://www.extension.umn.edu/garden/diagnose/plant/annualperennial/zinnia/leavesblotchesorspots.html
The leaf spot disease can be managed by buying disease-free plants, by spacing plants to increase air circulation, and by avoiding overhead watering which can splash soil-borne pathogens on to leaves. You don't need to pull out the plants, unless they become really damaged.; however, you should remove the plants at the end of the summer and burn or compost them (the bacteria does not survive winter).