5. Ellis Island is Half in New York and Half in New Jersey

The borders of Ellis Island have been contested since the early 1800s, coming to a final head in a Supreme Court case in 1998. There it was ruled that the areas constructed by landfill after 1834 belonged to New Jersey, this includes the entire abandoned side.
This decision means that some buildings are both in New York and New Jersey, so in practice the two states share jurisdiction. The island is federal property however, and the United States government is fiscally responsible and on the hook for maintenance.