To avoid spoiling the pesto flavor by the food processor, take care to minimize the heat produced by the blade. Some suggest chilling the blade and bowl assembly in the freezer before starting and monitor the amount of time the pesto is being processed, but it doesn't take that long to make a batch, and we haven't tasted a noticeable difference with not freezing the blade and bowl.
Using cheese fresh from the refrigerator helps control any heat as well.