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.
Contested Sequel: StarTropics II was about time travel rather than messing around in the tropics, and some fans of the first game didn't like the change.
Demonic Spiders: Those freaking gas mask robot raygun alien things in the last two levels of the first game. Durable, damaging, long range attack... argh.
Ethnic Scrappy: Baboo. The developers refrained from giving him a goofy accent, but appearance wise he's practically a caricature of a native islander. Fat, wild hair, grass skirt...
Fridge Logic: If Dr. J is such a good friend to the villagers of C-Island, why is his lab on the other side of a cave full of monsters from their village?
That cave wasn't always full of monsters. It's suggested that prior to Dr. Jones's kidnapping, it was just an ordinary cave with only tame creatures in it, and whatever kidnapped Dr. Jones also caused the monsters to appear in the cave.
Goddamned Bats: A lot, especially in the sequel which has numerous flying enemies, enemies invulnerable to frontal attacks, and especially the damn slimes that jump diagonally.
The Knight Rider, the boss of the first dungeon in chapter 8 of the sequel, is a major pain to fight. He moves quickly back and forth across the room while you're on a rapidly moving conveyor belt trying to shoot at him with limited range weapons.
The Dragon, which you have to jump to hit, can fly around blanketing the room in flames, and has to be fought under a time limit.
Chapter Three runs you through a series of five consecutive dungeons with few healing items. The longest and most difficult of these is the Ghost Village, which also includes several false exits to further vex the player.
After leveling out a bit for a couple chapters following Ghost Village, the difficulty spikes once more in Chapter 7, with enemies suddenly dealing much more damage and able to hit you from a far greater range due to being equipped with ray guns and other such weaponry.
They Changed It, Now It Sucks: The Happy Video Game Nerd makes the argument that the changes in the control scheme from StarTropics to Zoda's Revenge is one of the reasons the game is horrible (at least, in his opinion; he acknowledges in his Zoda's Revenge review that just as many people disagree with his opinion as agree with him).