Broken Base: Fans who remember the original straight-forward NES translation were generally disappointed with changes made in the remake's localization: the addition of 'regionalism' which brought ridiculous broken accents in the dialogue, and the changing of most names of people and places to make cultural references or bad puns.
Ensemble Darkhorse: Psaro, who gets his Heel Face Turn moment in the DS remake; Alena, who has a manga feature her as a main character and a game loosely based on her and her two helpers; and Torneko, who has his own series of Mysterious Dungeon games.
Les Yay: Elisa/Celia gets some fun dialogue in the beginning of Chapter 5 if you choose to play as the Heroine Sofia.
In Femiscyra/Gardenbur, the elderly priest thinks Sofia is jealous of his being the only functioning man in the whole queendom, and asks if she or one of the other female characters is one of those 'modern women'.
Squick: Psaro's growth of limbs and a second head/face is pretty icky in the NES game, but is just gross looking in the DS game. In a good way. Made even cooler as the DS version shows this from multiple angles. It really shows just how "not right" his transformation is.
Tear Jerker: The prologue's conclusion in the DS version, and the final boss's transformation the result of another tear jerker.
Also, Rose's death. While the NES version had the scene and its dialogue too rushed, and it sounded more like Rose is screaming when she dies near Psaro, making it less of a tear-jerker, this scene in the DS version is so much better, and the dialogue is not rushed anymore, making the scene when she dies quietly in Psaro's arms so heartbreaking.
That One Boss: Estark in all versions, Foo Yung and Chow Mein in the remakes.
Keeleon (NES name)/The Marquis de Leon (DS name) in all versions and Balzack in the remakes have always given veteran players trouble.
Viewer Gender Confusion: Thanks to a Manual Misprint in the instruction booklet for the NES version, it was believed that Panon is a female; yet when you do meet Panon (and talk to some villagers) in the game itself, the comedian is actually a man! But with the sprite for the Panon character in the NES version, it was hard to make out if he is a man or not. The Nintendo DS and PS1 versions thankfully cleared up the confusion by making better sprites for the character and renaming him as "Tom Foolery".