I don't know anyone close to me that currently has a puppy, so playdates, as it were, were not an option for me. My pup also had some leash reactivity to other dogs early on, so I really needed to introduce her to other dogs (IMHO). So, off to the dog park we went.
When I first visited, I kept her isolated from the other dogs by utilizing the small dog/puppy enclosure. We started this AFTER she'd had all of her vaccinations at around 5 months. At 6 months I let her go into the main area with the older dogs, and yes, she got rolled over and or ran over a bit. But it didn't seem to bother her at all, so we kept at it. At 9 months now, it's her favorite place in the whole world! We go daily, and she has her own little circle of buds to play with.
I agree with what others have said about timing and in our dog park that definitely rules out late night excursions, as several people bring their less-than-social dogs late at night.
In the 4 months we have been visiting the dog park I have only seen a couple of dog fights, and the owners swooped in quickly to break them up. I have not seen any dogs get hurt, though one owner probably did get some stitches because he chose to grab for a collar to pull his dog out of a fight. The dogs were fine.
I "thought" my puppy had pretty good recall before going, but noticed that her memory of such things sort of went away at the dog park. Puppies go through many stages as they grow up as well, getting rebellious at times, and that's pretty natural. If you wait until your puppy will recall dependably under any circumstance, you won't be going until much later on. But, for my puppy at least, she would still recall pretty well once I got close enough to her, so I didn't worry too much about that. IMHO it's actually a good training environment. At 9 months my pup will recall 100% from anywhere in the park, whether she's chasing and or playing with other dogs or not! I wouldn't be at all surprised if that changes again when she hits another rebellious period, but for now she's great in that regard.
There have been a few instances where I've had to intervene when another dog was picking on her and the owner wasn't paying attention. But I was able to break it up without a problem, so, so far at least, that hasn't been a big issue. I've also had to intervene a couple times when my pup was the offender...
But I frequently have more problems just taking her for walks in our neighborhood...with off leash dogs. I could go on about that, but I'll just leave it at that, hopefully your neighborhood is better about that sort of thing😉
I've seen lots of dogs come to the dog park here acting very fearful and timid, initially, and within a few weeks make HUGE strides forward in terms of sociability and confidence, so in that regard I think socializing with other dogs at the dog park for them was a great thing. My puppy too has "mostly" gotten over her leash reactivity toward other dogs, which is usually a fear response. And she's friendly to most all dogs big and small, which I don't think would have been possible for her without that exposure, so it has been a very good thing for her and her development IMO. She can now look at another dog, and judge whether to approach and play, or to avoid them. You cannot teach that to your puppy, it has to come from other dogs, and it will involve some less than pleasant experiences. It is, however, a life skill that may very well save you and your dog a lot of grief later on. IMO if you avoid other dogs until your dog is much older, they either will never learn that skill, or they'll learn it in a much rougher fashion than they would have as a puppy.
Obviously I can go on and on on this topic😉 But I will end by saying that if you're not one of those owners who just cuts your dog lose in a dog park while you browse Facebook or check your email, I have found the dog park to be an excellent source of learning for my puppy, and for myself, and I've met some very interesting people there as well.
It's not the size of the dog in the fight, it's the size of the fight in the dog. Mark Twain