Final answer:
The positioning error that has occurred when an AP image of the hip shows the lesser trochanter in profile is that the foot was externally rotated.
Step-by-step explanation:
When an AP image of the hip is acquired, the proper positioning should not usually demonstrate the lesser trochanter in profile. The presence of the lesser trochanter in profile indicates that there has been a positioning error. The specific error in this case is that the foot was externally rotated. When the foot is correctly positioned, it should be only slightly internally rotated (about 5 to 15 degrees) to bring the femoral neck parallel to the image receptor and prevent the appearance of the lesser trochanter in profile on the AP view.