The title of the movie says that someone "bought" the Moon. However, in the actual movie, that character describes how he gained the ownership of the Moon by using it over a long period of time without anybody else objecting to it - this is known as "usucaption". Usucaption is a distinct way of gaining ownership over things that is in many ways the exact opposite of buying/purchase. Purchase is a contract in which one party transfers ownership over a thing to another party in exchange for money. This would imply that the Moon had a previous owner who voluntarily gave it away in exchange for money, which never happens in the actual movie.
The final scene is set in the present day on the surface of the Moon and it depicts the US flag planted by Niel Armstrong in 1969 as brand new and with vibrant colors. However, in reality that flag is bleached white and in poor condition due to decades of exposure to solar radiation.