Americans Hate Tingle: Despite being voted as the favorite heroine in the famous Japanese magazine Animage, Nadia herself has had her fair share of detractors (DVD Verdict's Joel Pearce, in particular has called her "one of the worst heroines of all time"). Even certain critics have found the Grandis Gang annoying.
Big Lipped Alligator Moment: The Island/Africa episodes (23-34), save 30 (well, parts of it anyway) and 31. All you need to know about them is: Jean, Nadia, Marie, and King wash up on an island and meet up with Grandis, Sanson, Hanson, and Ayerton on another island. At this point, one can watch 30 and 31 and skip right to 35.
Also the sequel movie, which was not produced by Gainax, has nothing to do with the original plot, and recycles over half an hour of footage.
Ooh, Me Accent's Slipping: In ADV's dub, Jean speaks with a French accent which is noticeably inconsistent in at least the first couple of episodes. Keep in mind, though, that his actor was only twelve years old when he did the part, and otherwise the accent works in favor of the character. He gradually improves on the accent as the show progresses (the actor admits it took him several episodes to really get the hang of it).
Critics have often (and unfairly) attacked the ADV dub, declaring it "unlistenable" on account of the accents alone, never mind that this is a show where the characters are supposed to be European. To the average listener, however, the accents work in favor of the story, and other critics, like Bryan Hensen at Anime Jump, Ryan Matthews at The Dub Track, and Brett Barkley from Mania all commended the dub, overlooking its accents and acknowledging the solid performances throughout.
It should also be noted that some of the characters Nadia, Marie, Hanson, and the Sonar Officer speak with neutral accents in the ADV dub. (The dub directors said that this was to work in favor of Nadia being all over the world and not having had time to adopt an accent.)
That's nothing. Marie (about 5 years old for the main story) is pregnant and married to Sanson!! Though he did wait until she came of age.
What Do You Mean, It's Not for Kids?: Despite its generally lighthearted narrative, there are many scenes (and several episodes) that are decidedly dark. Several characters are executed onscreen quite graphically, the heroine tries to commit suicide at one point, and later, shoots her father, Nemo, while under Gargoyle's control. There's also a brief instance of racism and, near the end (between episodes 30 and 31), Nadia spends nearly two full episodes nude.