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....
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.