How can I prevent rain from dripping off the roof rake edge?
That is not unusual if you live in an area where the wind /rain are blowing at an angle to the home. Even with no real wind it can happen and a photo would be helpful. It may be a slight difference in the stagger of the shingles or possibly the overhang has a slight sway or droop there we usually leave a bit of an overhang on the sides and I probably would not worry , but a photo might reveal an issue that we can point to.