Anticlimax Boss: Unless you're really playing with the worst possible duo to fight that boss. Kabutops and the Omastar brothers in the Brine Cave are dramatically hyped-up in-story as "vicious Pokemon" that Chatot and Wigglytuff barely managed to survive encountering in the past. They also take out Team Skull effortlessly. They all happen to be Rock/Water types though, so if you or the partner is a Grass type, the battle is pathetically easy. Even some Fire type starters can win the battle without much difficulty, especially if they're able to exploit the Rock type of the ennemies, for example with Fighting-type moves (Focus Punch can deal massive damage to them, if not one-hit-kill the Omastar brothers.
Critical Dissonance: Critics gave it a tepid-at-best reception. Fans on the other hand have given it Cult Classic status for its powerful and moving story, and it is widely considered to be among the best Pokémon spinoffs.
Cult Classic: Due mainly to its narrative and a soundtrack brimming with great music, this side-game has almost as many fans as any entry of the main Pokémon series, and it still remains a popular and well-regarded game even years after its debut—if anything, after some Contested Sequels in both the main franchise and the Mystery Dungeon subseries, it's gotten more popular with time. Sky in particular is well-regarded for adding in the Special Episodes, increasing the number of playable Pokemon, and letting players experience the soundtrack whenever they want with the Sky Jukebox.
Demonic Spiders: Purugly in the Hidden Land. They have Fury Swipes, which is already annoying when you consider multi-strike moves are Game Breakers, and Swagger, a confusion-inducing move that boosts your attack so you're likely to miss or hit your allies.
Pretty much ANYTHING in Temporal Spire. Specifically, the Porygon-Z who have Discharge which will hit you no matter where you are for really high damage which you likely won't be resistant to, and use Agility to boost the speed of every enemy in the room, meaning a Mighty Glacier like Salamence will now hit twice as fast. Salamence and Metagross also hit like trucks and if you're weak to Psychic, Dragon, Steel, or Fighting, you'll die really quickly to Bullet Punch, Psychic, Dragon Claw, and Meteor Mash respectively.
Ear Worm: Aegis Cave. It doesn't help that Aegis Cave is the setting for a particularly time-consuming and tedious mission.
Even Better Sequel: Although both Explorers and Rescue Team were received about the same by critics (that is, lukewarm), most fans agree that Explorers has a better storyline and character development. The fact that the bond between you and your partner doesn't dissolve after the credits play helps a lot too.
Doubly so for the Sky version, which averts the One Game for the Price of Two elements from Time and Darkness, brings more starter pokémons, adds a handful of side-stories for more character depth, and introduced a few aspects that, much to the chagrin of the fanbase, weren't used again in future sequels, like the Spinda Bar and the Lookalike 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.
The randomly generated food in dungeons would give inhabitants of the Bad Future some things to eat, but since food still isn't quite plentiful, it's very likely that starvation is an issue for many Pokemon. Notice that in the dungeons in the future, nearly 1/3 of the encountered enemy species are Ghost-type...
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.
In Sky, most evolutionary families get a 3-star exclusive item that, when in the inventory, has the Pokemon healed by damaging moves of a certain type, instead of taking damage. Said type is usually one that would deal super effective damage otherwise, but there are exceptions. One of such is the Bronzor evolutionary family, who get healed by Ghost-type moves, which dealt neutral damage to them. Fast-forward into Generation VI, and now Bronzor and Bronzong are indeed weak to Ghost-type moves thanks to the changes in the type chart.
Two localization-only examples. Koffing, Zubat and Skuntank's team was named "Team Skull" in the English version, which ended up being the name of the villainous team in Pokémon Sun and Moon. Similarly, "Primal Dialga" (who was called Dark Dialga in Japan) became this after the remakes of Pokémon Ruby and Sapphire introduced Primal Reversion.
Paranoia Fuel: A conversation with your partner about killing yourselves ends abruptly as the two of you go to sleep. When you wake up, your partner's bed is empty.
Player Punch: The ending of Special Episode 2 in Sky, Igglybuff the Prodigy. Igglybuff has befriended his loyal, trustworthy master (a retired explorer), they've explored and found heaps of treasure. Then, after they beat a remote dungeon, Igglybuff's friends and parents turn up to reveal that Igglybuff's mentor, Armaldo, is actually a B-rank outlaw. You can practically see Igglybuff's world ending as Armaldo's taken into police custody.
Can be considered a Bittersweet Ending as well, due to Armaldo's changes in his behavior hinting that he legitimately wants to clean his slate at the end, after spending so much time with a child like Igglybuff. The ending of the chapter all but spells it out.
Rescued from the Scrappy Heap: Most of Chatot's detractors (especially over the Perfect Apple incident) were rather impressed by his actions in the Brine Cave.
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.
Sequel Displacement: While not as bad as some examples of this trope, some believe that Explorers of Time/Darkness/Sky were the originals and don't know about Red/Blue Rescue Team or just ignore them.
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.
That One Boss: Palkia can be troublesome too, if he feels like spamming Spacial Rend. It also hits the whole party, and unlike Dialga's Roar of Time, he doesn't have to spend a turn recharging.
Dialga can count too. though he has the turn-recharging drawback, it hardly comes into play if his Roar of Time can outright kill either one or all of your party members at full health.
Temporal Spire may perhaps hold one of the most punishing difficulty spikes in recent years thanks to a myriad of reasons. The penultimate stage of the main story only allows you and your partner in, meaning if either one of the two are any sort of weak to the many traps and strong Pokemon in the dungeon, then grinding for experience or for items will be the norm until a winning combination has been made.
Any of the Legendary dungeons, i.e. Bottomless Ocean, Giant Volcano, etc.
Mt. Bristle can be a bit of a challenge for the sole reason that you're not quite strong yet. It's not helped by the fact that Drowzee might be a bit of an Early-Bird Boss, if you get unlucky and his Forewarn ability activates a lot or if you or your partner are weak to psychic attacks.
Tier-Induced Scrappy: Cresselia is perhaps the worst when it comes to this. Not only do you have to escort her to the end of the dungeon (which contains tons and tons of lava for her to float over and burn herself with), but she also takes place in the final battle against Darkrai.
That being said, she at least has the Lava Evader IQ Skill, so she won't go onto the lava on her own.
They Wasted a Perfectly Good Character: The role of Giratina. You would think that Giratina would be the game's True Final Boss, what with being the Pokemon stronger than both Dialga and Palkia, as well as having a pre-established relationship with Dialga, Palkia, and Arceus. Obviously, if the game were to have a greater villain, Giratina would be the one, right? Nope, Giratina is a mere treasure-guarder, while Darkrai, a lesser legendary with the same stat total as Goodra, no relation to Dialga/Palkia/Arceus, and no plausible way to overpower the likes of Dialga is the True Final Boss.
The partner, after the player disappears. Or them in general? For one, they're a young Pokemon (presumably a kid) who's also a coward who only got the strength to join the guild from the player, they've gone without dinner because of Team Skull, they were bullied by Team Skull in general, and their best friend/life partner disappears into light before their eyes, leaving them to go home alone while barely being able to hold themselves together. Things seem to be looking up for them when they return, only to have Cresselia (actually Darkrai in disguise) tells them to kill themselves along with the player because they are an anomaly. Ouch.
What about The Player themself? For starters, they're an amnesiac from the future who has lost their family and turned into a Pokemon. Especially when finding out they exist only because of a bad future and they'll disappear once Primal Dialga is defeated. Pretty much everyone from the Bad Future could qualify, except the Sableye and Dusknoir. Grovyle for being an idealist who wants to change the past even if it means he won't exist, Celebi for using most of her energy to send Grovyle, the player, and your partner to the present day and risking being murdered by Dusknoir's Sableye. It only gets worse after the post game story where Cresselia (actually Darkrai) asks you and your partner to kill yourselves to save the world, you're hunted by a well-meaning Palkia, and nearly killed by Darkrai in a nightmare when you dare to interfere with his plans.
Manaphy could also qualify being a baby who ended up living away from his adoptive parents (you and the partner), and missing the sea despite the fact he enjoys being with you.