1-2 Starts does nothing, 3 Stars triggers the "Story Credits" event (only once), 4 Star supposedly has a small chance at letting a Jacob's Ladder grow in your town and 5 Stars grants you the Golden Watering Can DIY recipe and allows Jacob's Ladder to spawn more frequently.
Good to know. I won't bother maintaining my 3-star rating now that I got the K.K. Slider event, since I reached it by putting a bunch of random stuff all over my island. ^o^;>