Pros:
The course is set in a nice city park. As others have said, it is a good course for players of many different levels. Newer players will enjoy the shorter holes and losing a disc is unlikely. Experienced players will still enjoy the challenges and will have many birdie opportunities. There is a decent amount of variety here from hole to hole, each hole was relatively unique from one to the next, little repetition in appearance off the tee. This course is designed to be fun and enjoyable.
Cons:
This course was extremely crowded when I played. We had to wait in line on Tee #1. It was pretty congested for the first few holes, but it opened more after that as the course spreads out and the holes get a little longer. From the other reviews it seems this course is popular and usually busy. It would not too long to play 18 if the course was empty, but plan on having to wait on a few tees. The first few holes are close to each other, almost seem to cross each other (but I think some people were playing to the wrong basket, which is understandable), so be on the lookout for errant throws.
Other Thoughts:
Shillito is not a bad course, and is perfect for locals who are newer to disc golf and are learning to take their game to the next level. There are many pro level courses in KY to choose from, so skip this one if that is what you are seeking. It does provide for a nice contrast, however, and has its place as part of the group of courses in the Lexington area.