Your puppy's relationship with adult dogs
Adult dogs will expect good canine manners from your puppy as he matures. If they don't consider his behavior appropriate for his age they won't hesitate to let him know his behavior is not acceptable. For example, if your puppy is racing around and bumps into an adult dog his behavior will be corrected. Bumping into an adult dog is rarely accidental and most adult dogs know this. Adult dogs will also react to any assertive behavior from your puppy, for example, putting his paws or his head across the shoulders of an older dog.
If the adult dogs are well socialized and stable their reactions are usually appropriate. They should not be overly aggressive with your puppy but may discipline him with a growl or a snap. Puppies learn good canine manners from adult dogs. As long as it doesn't go any further than a growl or a snap you don't need to intervene. Note, if many of the adult dogs at your local dog park seem to be "picking" on your puppy, chances are good that your puppy is being rude in canine terms, and drawing their communal attention.
Your puppy's relationship with his peers
You may notice that play between your puppy and puppies of the same age becomes rougher as your pup matures. Let loose, in a large and enclosed area, your puppy may tear around playing chase with his buddies. You'll know this is all in good fun when the puppy being chased changes occasionally – it should not be the same puppy all the time. If the one being chased repeatedly attempts to hide, and does not appear to want to play anymore, then this game may have switched over from happy into hassling. If you see this, intervene. If the chased puppy comes out of hiding and invites more romping, then all is still well. If not, then it is time to end that particular game for the day.
Your puppy's relationship with younger pups
As your pup's status changes, he may begin trying to assert his newfound authority on those who are lower in the group than he is. This is often puppies from five to eight months of age, puppies younger than your puppy. Your pup may pin younger pups, knock them over, or make the younger pup nervous by simply being too intensely attentive. This is particularly true if your older puppy was not socialized with other pups when he was younger.
Don't encourage this behavior – when you see this happening call your pup to you. Move him off to play with another group or use some commands to distract him. If it is a consistent problem, arrange for your pup to only play with dogs who are older than he is.
These changes in play are normal and to be expected. They mark your puppy's continued development. Adulthood is not far away now.