Traditional olive (Olea europaea) orchards have been grown for thousands of years and still occupy most of the world’s cultivated olive areas. To compete with olive oil produced in the higher-yielding intensive orchards, the oil from traditional orchards must be of high quality. We evaluated oil quality—potential and actual (under commercial conditions)—and tested the stages in the production chain that are likely to reduce oil quality in the traditional sector in the Middle East region. Our findings show a clear negative impact of growers’ traditional practices on both the chemical and sensory characteristics of olive oil. The oil originating from the commercial process had higher free fatty acid and lower polyphenol and carotenoid contents, lower stability, lower pungency, lower fruitiness, lower bitterness, and a higher prevalence of organoleptic defects than oil that originated from fruit picked from the same trees during the experimental procedure. The current common harvesting technique of pole beating significantly increased fruit injury and fruit with mold, leading to a reduction in oil polyphenols and an increase in free fatty acid levels compared with those resulting from manual picking. In addition, after harvest, storing the fruit for more than 48 hours in plastic bags dramatically reduced the oil quality. The traditional olive orchard could be a source of high-quality extra virgin olive oil. However, fruit handling—from the trees until the end of the oil extraction process—is performed incorrectly, thus adversely affecting the oil quality.