This is a phenomenon called stippling.  It is caused by insect feeding on chlorophyll.  Typically, it won't hurt the plant, but it looks bad.  The rosemary can still be used for culinary work.  

Things like leafhoppers, spidermites, lacewings, algeids, and aphids are candidates.  

They can be treated with  neem oil, capsaicin or pyrethrum or cabaryl.  If treating, make sure plant is not in bloom...If it is, wait until it is no long in bloom before treating because they products will kill pollinators.  

Hope this helps.

r/Mart