It's special because the PLO is not a sovereign body, that is, it is not a national or supra-national body like other countries or the United Nations or European Union. The Sovereign Military Order of Malta is headquartered in Rome, and is "widely considered a sovereign subject of international law" [according to a quote in Wikipedia].
Although the Palestinian National Authority was established (by the PLO) in 1994, the PLO Executive Committee performs the functions of the government of the State of Palestine. Currently, the PLO maintains a network of offices in foreign countries and also represents the PNA abroad [Wikipedia]. Thus foreign relations are maintained with the PLO rather than the Authority.
It may also be considered special because neither representative resides in the territory of the other. The PLO representative is in London, and the Apostolic Nunciature is in Tunis.