Right now Flying Unicorn is the only thing closed. Also the entrance to Dueling Dragons is now in Jurassic Park and the area is kind of a mess but everything else should be open for the time being.
Whats going on with Dueling Dragons? Is it being re-themed? Has the entrance permanently moved? I can see how they can quickly make it HP themed by using the dragons from the Goblet of Fire but I haven't heard anything definite.