There definitely are implications here. If you use references to any of the things that Rowling originated, such as Hogwarts, the Golden Snitch, Quidditch, or any of the specific characters, such as Harry Potter, Ron Weasley, Hermione Grainger, you may be in for a rude surprise.
Certain things will be in the public domain; for example, Merlin is in the public domain. Dumbledore is not. Basically, you should avoid specific references to HP material. You can use general references to wizardry, witchcraft, spells, potions, etc.
This kind of thing occurs every time there is a new hero with magical powers or very popular kid's icon. The way the people who own the licenses to these things catch the violators is that they go through the local phone books and say things like "I'm giving a birthay party for my 8 year old son, and he is a very big Harry Potter fan. Do you do a Harry Potter show?"
If you say, "Oh, yes. I come in dressed as Dumbledore and give every child at the party a diploma from Hogwarts and a golden Snitch," then prepare for a visit from the trademark police. If you say, "I do a show that is geared towards a wizard school. I dress as an old wizard, and during the show, I put a school robe on the birthday child and the other volunteers who come up to help me. When the show is over, they get a diploma from the Academy of Wizardry," then you are probably going to be okay. You can always add "because of copyright and trademark restrictions, I can't actually be a character from the Harry Potter movies, but I can still be a wizardry instructor and do some really neat things along that line."
That will probably get you off the hook.
About 2 decades ago, there were lots of people performing as Barney. A lot of them were busted when the Lyons group had their people phone the folks who advertised in the yellow pages. Now, it's even easier, because you can google Harry Potter birthday party and find out who the violators are.