@Rozzak All a Mary Sue is really supposed to do is be too good at everything and even upstage the actual main character(s) at everything they're good at, because the original use of the term was applied pretty directly to self insert characters in fanfiction (the name itself comes from a parody of such characters in Star Trek fanfiction iirc).
A lot of the characters that get called Mary Sue/Gary Stu/the other thirty variants of the names, should probably just be called self inserts or proxies. Slightly less specific terms that still possibly apply, like here. Rudeus might largely be a wish fulfilment self insert/proxy character for the author or the readers, but since he always has been the main character of this story I feel like the Mary Sue term shouldn't apply. Then again, this could also be another instance of meanings evolving over time. Language really likes to do that in ways that just muddy the waters on specifics.
'supposed to' is incorrect, some gary stus do make mistakes, but they are less common.
Rudeus can be considered a gary stu at times but he definitely isn't always a gary stu: for example, the trio kid gang in demon continent dying because of his inaction definitely did not endear him to the audience.
I agree with JaddyZyato that he is the most gary stuish during the school arc, but it's partly because Rudeus being a strong magician stands outs more in a magic school, in which the students are around his age.
@SuppaTenko It's one of the original facets of the character that turned it into a term. Like I said, the whole thing spawned from poor characterization in fanfiction being made fun of via fanfiction. The character, Mary Sue, was an absurdly young Starfleet lieutenant who was better at everyone's jobs than they were. She died tragically in the line of duty, after rescuing some of her fellow fleet members, while the real main cast cried at her bedside over the loss of this ridiculously competent fifteen year old girl that some of them wanted to fuck.
Huh, the art in this issue had some intriguing hints of Maybe, esp. the eyelashes in p.7 panel 3, and the facial structure in p. 12, panel 1. Coincidence, or is Fujikawa Yuka part of Maybe?