The dog park is located in the Waterfront Park on the Southside just under the Birmingham Bridge. There is a small and big dogs section. The small dog section still has nice grass, but the large dog area is well trampled. New woodchips would go a long way.
There are plenty of benches boasting nice views of the river and city.
I have not seen any dog fights yet and most owners seem very responsible. Occasionally, someone brings their grocery bags from home and water bottles and bowls, just in case you forgot yours.
Finally, there is a pleasant trail where I take my dog down to the Hot Metal Bridge. Haufbrau Hauss is down there, but you cannot take your dog into the biergartenn :(
All in all, a few cosmetic touches and a dog bag dispenser would take this place to a five star level. An additional bonus would be one of those anerobic digesters/street lamps that creates light from dog poo.