Although rosemary resists most diseases, some cases of powdery mildew have

been reported. I have heard of five different strains of powdery mildew that can affect rosemary.  To prevent the disease from spreading, check the plants regularly and apply the proper fungicides when needed.  Rosemary should receive at least 6 hours of sun each day; it grows best in full sun.

Rosemary is fairly resistant to pests. If spider mites, mealy bugs, or scales do appear, any organic or inorganic insecticide may be used.If the plant has scales, an easy solution is to clip off and discard the infested plant tips; scales are sedentary insects. For mealy bugs, spray the plants with water, pyrethrum soap, or a soap-based insecticide. Insects that suck plant sap are generally more prevalent in areas where too much nitrogen fertilizer has been applied. You can avoid most insect problems by fertilizing properly.  There is a beetle that will eat on rosemary but I have not confirmed seeing the beetle here.