The Mastermind of Mirage Pokémon
This special was made to order at the behest of The Pokémon Company International, as a result despite being produced in Japan, it aired first in the United States. When it finally did air in Japan it did so just after the start of the Diamond & Pearl series, despite featuring characters from the Advanced Generation.
Even trying to place it using the US airdate, there’s still continuity issues.
The airdate places it just after AG136, however Pikachu uses Volt
Tackle, a move he won’t learn in the anime for another thirteen
episodes.
Taking Pikachu learning Volt Tackle as a starting point, the next limiting
factor is that May’s Combusken evolves in AG191 so it must take
place before that. Unfortunately this results in a huge fourty episode window
in which MoMP could have taken place.
Given the lack of other landmarks to help place it, the concensus seems to be to place it as early as possible in that window, that being closest to where it aired in the dub’s broadcast.
Source: GameFAQs Pokémon Message Board