These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Logic: In a world where the sun never shines, the water doesn't flow and the seasons are non-existent, how do the native Pokemon stay alive when their food sources are frozen in time and thus can't grow anything?
Maybe Celebi uses the Passage of Time to travel to the past and get whatever food and water they need.
Apples, berries, and seeds randomly generate in the future dungeons just as well as they do in the past dungeons. Whether or not this is some kind of weird Gameplay and Story Segregation may be up to interpretation, though.
Good Bad Bugs: Occasionally, when winning big at the Recycle Shop, the prize is a higher tier ticket. You can receive and redeem it even if the shop doesn't offer the tier yet.
He's Just Hiding: A fair portion of the fandom's reaction to Grovyle's disappearance near the end of the main arc. What actually happened to him was later revealed in Special Episode 5 of Explorers of Sky.
Scrappy Level: Who in the hell thought the Aegis Cave challenge was a good idea? At some point in the after the end, your team will be required to go to a dungeon called Aegis Cave. To get through, you must solve three word puzzles by spelling out ICE, STEEL, and ROCK. In order to do this, you must go through each dungeon and fight multiple Unown who might drop a corresponding letter stone for you to spell these words with. Might. You will inevitably have to go through each of these dungeons multiple times to get the correct letters. And this challenge is mandatory.
Best part? If you want to go back to recruit the legendary golems, you have to spell out the words all over again. And you might not even recruit them on the first try.
However, you can use the Wondermail Generator to get codes for jobs that will get these items. It's still annoying, but better then what you have to do otherwise.
Rousseau Was Right: Wigglytuff seems to believe this, given it's him that says "evil pokemon don't really exist in the world".
Tear Jerker: The ending cutscene. All of it. Your character disappears before your partner's eyes, leaving them staggering towards the Rainbow Stoneship alone. Several months later, they find themselves on the very beach where they first met you...and end up breaking down in tears after remembering all the adventures you had.
The Woobie: Bidoof, especially seen in his special episode.