I read that she was afraid of flying somewhere, yet in an episode of Stars, she's on an airplane and not scared at all. A mistake by the animators?

Firstly, (ocd me) has to correct the name...it's Makoto. xD Secondly, I think she only mentions being afraid of planes in the manga not in the anime. So therefore, it wouldn't be a mistake.

But good catch! I never really thought about that. They don't ever talk much about her parents or how they died in the anime, so her manga-fear of planes is never brought up.

You could always say at that point, for the Three Lights she got over it (plus she's spent a few years as a kickbutt soldier of justice so she's possibly gotten over any pre-Soldier fears). xD

A thought just occured to me about that, actually. If she still had the fear of planes in the anime, and she was introduced before Jedite was defeated, Makoto would have had a nervous breakdown during the airport episode.

Duh, I can't believe I spelled her name wrong.
Anyway, I believe stories should be fairly consistent with the original material, so if she's afraid of flying in the manga, she should be in the anime as well.

not necessarily (though your misspelling makes a great sounding daughter name for her xD). its well established that all versions of sailor moon are their own thing and follow their own canons. while the anime is based off the story of the manga it takes its own liberties with the story and characters. just because a manga comes first doesnt mean it has to be exact.

most likely what happened is the bit about makos fear of planes had not been shown in the manga during the writing process of the anime (especially since it aired mostly simultaneously with the mangas serial release) plus its only mentioned once in the manga and never brought up again.