Complete Monster: Daos, deciding to send a message to mankind of "real terror", warps Maxim to the town of Chaed, then uses his island fortress to blow up it up, killing everyone, even children, while leaving the heroes alive solely so they could feel the terror as the humans around them died. Daos then orders the kidnapping, and attempted murder, of Maximís infant son, Jeros. He later decides to destroy the human world, leaving his followers behind.
If you have the money for it and sleep at an inn, they will charge you the normal price. If you don't, you sleep free.
The Egg Dragon has its HP set at the Cap, but the programmers didn't set a maximum HP value. As a result, using any sort of healing on it will overflow its HP, leaving it weak enough to finish with a single hit.
Capsule Monsters were far, far easier to feed in the American Version than other English versions. The first upgrade could be done with 11 Long Knives and 40 Shrieks which is far cheaper than any other means, for example. Feed them 1 knife, then 3 Shrieks, then 1 Knife, 3 Shrieks. The other English versions seems to have fixed this "bug" (or at least tweaked the algorithms). Too bad the Cave and Submarine Shrine have messed up graphics in the American Version....
Tear Jerker: The deaths of Maxim and Selan; even though you know they're Doomed by Canon since the beginning of the first game, it hurts so much more when you've gotten to know them better over the course of the entire game. The entire ending that follows is just as sad, with Tia crying for the first time since she was a child as she senses Maxim's death, and Selan's aunt telling their son Jeros that they'll be home soon after saving the world, unaware that he's now an orphan.
That One Boss: The Tarantulas, though weak to fire, can be a real pain due to the fact that it can inflict poison and paralysis. It can also summon spiders to assist in battle.
That One Puzzle: The third Reversi puzzle in the Treasure Sword shrine, in the non-Japanese versions.
That's to say nothing about the "World's Hardest Trick", the sliding block puzzle in one of the last mountain areas in the game. Also worth mentioning is the 'weak floor' puzzle in the Phantom Tree Mountain, and the 3x3 bomb square grid in the dungeon near Dekar's castle.