The welsh situation is I think a historical one that would be difficult to unwind.The whole United Kingdom situation in FIFA has a long political history .European countries have always questioned the separate memberships of England , Scotland,Wales and Northern Ireland , when they are one political entity (sort of - Scottish separatism , etc).
There are a couple of other situations that spring to mind - Leichenstein /Switzerland maybe ?
The Nixs participation is the A League was only ever approved by AFC (Bin Hamman and his corrupt mates) on the basis that NZ did not have a professional league.The confederation thing complicates it but the lack of a professional league was the deal breaker.