Ash either wins or comes in second, while Paul only makes the top 16. Ash heads to new territory with Pikachu and Bayleef, while Chimchar enjoys being pampered by Tracey. Charizard makes a few trips to visit them now that his training isn't quite so intense. Ash continues to mature, but still is a bit hasty at times. He is curious about the whole Aura thing, but nervous enough that he doesn't jump into it as quickly as usual, resulting in a slow buildup of his skills. (In other words, he doesn't pull a Willow.)
Brock takes a more active role now that Ash is being portrayed as old enough to not always letting his enthusiasm get the best of him. Croagunk stays with him in the new area, and Crobat returns. Brock's little brother (Forrest?) is able to catch his own Pokemon and run the gym, so Brock can now switch out his Pokemon if he feels the need.
Dawn doesn't win the GF. However, she does do well enough that she feels satisfied for now and knows she's got something to work toward. She joins Ash on his journey to the new area, even if there are no contests, because it will help her work on her skills outside of contests.
Jessie also doesn't win the GF, but still does well enough that she doesn't throw a diva fit at losing. She starts to reconsider her membership in TR, wondering about concentrating on contests instead.
James continues to follow Jessie, and eggs her on with the contests. He's also getting sick of the whole TR bit.
Meowth, on hearing that Giovanni retired Persian only to replace it with a Glameow, has a catfit (sorry) and starts agitating for them to quit.
The threesome as a whole decides to quit TR, and sends Giovanni a parting gift that infuriates him to the point of sending a goon squad after them. Ash and Co. help send the goon squad packing, and when they return to Kanto, the whole lot of them make a personal visit and warn him off ever messing with them again.
Paul is utterly humiliated in his last Sinnoh League battle by a girl who nicknames her Pokemon and pampers them shamelessly. If she wears a lacy dress and has fluffy pink hair it would make it even more satisfying. This crushing defeat sends him over the edge and he becomes the new stalker villain, blaming his downfall on Ash and vowing revenge. He is a much darker threat than TR, and is actively trying to harm Our Heroes. He will not show up every episode, but they will always be aware that he is after them, even though they don't really understand why.
One of Misty's sisters sustains a major head injury that results in a complete personality shift: she becomes sensible and responsible, and cheerfully takes over running the gym so that Misty can travel with Ash, Brock, and Dawn in the new area.
Zoey and Nando both do well in the GF; Nando might even win it.
May goes to Sinnoh.
Max begins his own Pokemon journey in Hoenn.
Professor Oak marries Ash's mother, shocking Ash but nobody else.
Tracey is occasionally sent to do field work, and naturally runs into Our Heroes almost every single time it happens.
Hunter J continues to be Hunter J, and will be encountered in the new area as well. She will have a run-in with Paul and tell him his Pokemon aren't worth stealing- and then make a grab for Pikachu, as she has a client who will pay very well for a Pokemon that hides a lot of power under an unassuming exterior.
The GS ball will be discovered to have been a jewelry box made for a top fashion designer, but was lost when the plane it was on crashed into the ocean. The catch was damaged in the crash, which is why it wouldn't open, and the fact that it wasn't a Pokeball in the first place explains why it wouldn't transport. The reason nobody knew about the missing jewelry box is that it was made secretly for an upcoming fashion show, and the designer has been searching for it secretly ever since.
