For the longest time, something has been troubling me about the placement of EP081, "Pallet Party Panic" or "Masara Town! Setting off on a New Journey!", in Season One instead of Season Two. Here are some key points as to why EP081 should be considered as a Season Two episode.
Airing on January 28, 1999 in Japan, EP081 was the first episode to air with the theme song "The Rivals". replacing "Aim to be a Pokémon Master". Right away, this should mean something. And while this episode did air with the Season One Theme in the English Dub numerous times, it was changed to the Season Two Theme on the DVD, and as far as I know, also for later airings on TV. I think this definitely shows the change of season began in EP081 as the opening changed in both languages, which most commonly reflects the season itself.
If you saw EP080 and EP081, I'm sure you'll get where I'm going with this next. EP080 is basically the end of the Indigo League and would be a great choice for the final episode of Season One. EP081 on the other hand, begins the next season with the task of delivering the GS Ball. So wouldn't it make more sense with an episode like that to be at the beginning of a season and not at the end of one?
With these two reasons, I think I present a pretty solid case.