I saw and enjoyed the film, but so many years ago I can't recall sufficient to answer. Looking forward to your post with your observations.

I read the book.

Isn't the part where she got naked and woke up in the trashcans her major faux pas?

I just watched the movie and I can't work it out! Please post the answers. XD

This thread made me rent and watch the film ;-). Found it really funny, for the most part I was completely cringed at her! :-$ (Even if I can't really verbalize or rationalize why...) I don't know enough about Japanese culture, so I'm sure I'll miss some of the most obvious key points you wanna discuss, but here are some of my thoughts:

A) I understood that task not as a real one but as a punishment (in a similar way to the photocopier thing), caused by her actual first faux pas: not properly presenting herself and being late her first day, after a delay caused by her absent contemplation through the window, exactly where that boss found her some seconds/minutes later. (Also, as her immediate boss, 吹雪, was busy elsewhere, I guess it also was a convenient way of filling her time doing something "productive" during that morning). Maybe not at first, but in the end I felt very sympathetic for that boss: IMO he kept his hopes high on her for a considerable amount of time (if not for the whole film).
Anyway, during that punishment, or even if it were a real task, she had to be more humble and treat her boss with more respect than she did. Instead, she even smiled and laughed at times. In summary, her body language was never appropriate (I wonder if her verbal language suffered that as well, but in the film she didn't talk much during that scene).

B) I really didn't get it. What I felt is that she was too interrupting to the meeting. In her place I would've STFU completely, but not for any special reason. I believed at some point it was something the delegation's staff made up just to have an excuse to leave, but after reconsidering it that's unlikely the case.
I don't understand why, without telling her first, their bosses were expecting her acting as if she didn't knew the language, unless: a) it is expected of someone who serves coffee to strangers in a meeting to be completely mute, or b) her less immediate boss/bosses asked for her, specifically, because he/they thought she didn't speak Japanese, while her immediate bosses knew it but knew nothing about the reasons why she was chosen.

C) Not sure what you're talking about here. Maybe about the conversation with the same boss from A) right after B) happened? In that scene, while he was yelling at her, at the same time seemed understanding and as if he where trying to instruct here in Japanese culture, but she was too close-minded to get it.
Or, perhaps, you are referring to her last moments in the company, where she holds a meeting with 吹雪 to say she will no longer work there? About that, I'm still not completely sure her boss was really being sarcastic or sadistic.
In any case, my opinion is that her definitive fall from grace was her complete incompetence with relatively simple task (getting completely wrong what "GMBH" stands for, unable to adequately copy numbers from one piece of paper to another, unable to check some simple bills -even if she had to do some currency conversions-), all of that maybe motivated by being such a daydreamer and so sentimentally pissed off by numbers (all of this is just a conjecture of mine, of course). Being unrelated to her true abilities didn't help either.
From 吹雪's point of view, it is completely absurd, 'till the point she first thinks her subordinate is trying to sabotage either her or the company, and finally firmly believes she is handicapped. I wonder if the letter she wrote her saying 「おめでとう」 after the publication of her first novel was motivated because she actually thought it was a veritable achievement for a mental person .

Your position seems very understandable to me (after all, we are pragmatic gaijins, aren't we? ;-). That said, I suppose they find of the utmost importance the fact of being disciplined when working as part of a team. They probably also value more a good work made with honor than a great work made with diligence but faulty in respect to work ethics or hierarchies (there's another notable scene about that in the film, btw).

In my opinion, it's instructive to compare it to (occidental, for instance) armies, with their discipline and command chains, because a lot of those "alien" behaviors start to feel less far away from our own home, don't you think? And after all, even some of the vocabulary found in Japanese work culture comes from the military world, so I'd say it isn't by coincidence. Whether you are fine with that cultural aspect or not is another question, though.