On the first visit to the Hazel Parker dog park, I discovered it was still being worked on. Today (being the first day of vacation), I decided to head back over there and see what progress had been made.
The dog park is open now, and doesn't really look much different than when I was there last, aside from having operational dog-lock gates. They aren't latched though, but that may just be a temporary thing. Several benches strategically located underneath the trees provide a spot for people to sit and relax, and over in the corner is a water fountain.
Although the park is fairly long, it would still be pretty easy to throw a ball too far and out of the dog park, especially with the aid of a Chuck-it. The park would be very well suited for smaller dogs and dogs that aren't that much into running around. People with more active dogs would probably find more satisfaction (as would their dogs) heading to one of the larger dog parks like the one at Hampton Park or James Island County Park.