I think the number one thing needed for a dog park is a good off leash recall. I can't tell you how many times I've seen someone calling and calling and calling their dog over and over with the dog paying absolutely no attention whatsoever.
And this brings up a training issue. If you go to the park and think your dog has a good recall and it gets there and you call it and it doesn't come right away, please do not call it again and again. Do something (run away, jump around like a fool, pretend you're eating something, clap your hands....etc) to make it want to come to you. You are going to have to be way more interesting than all the funn buddies it has just met. Every time you call the dog and it does not come reinforces the fact that it does not have to right away. Also do not call it away from playing to snap the leash on and leave the park. Call it and release it to go back to play it's a great reward. Dog parks are great for training under distractions. I personally wouldn't take a puppy to one and let it off leash for the reason listed above (it's not fair to expect a young pup to have a perfect recall), but I would let the pup drag a long leash so that I still had control while the pup played.