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I have a flute piece marked as moderato, with a quarter note=76. But the piece only contains sixteenth notes, so it actually doesn't sound moderato when you play it.
Isn't the indication moderato in such a case somewhat inaccurate?

Thank you for your opinion!

Actually, I can easily imagine that sounding totally moderato, depending on the piece (and depending on the 'tone' and 'attack') -- and in fact I would think those notes at that tempo would usually sound moderato.

Maybe if you tell us what piece it is, maybe including a youtube link......

BTW: And if that speed doesn't sound moderato, I would suggest that you're putting it backwards in terms of what would be "inaccurate": more likely it would be the M.M. that's inaccurate, not the "moderato." IMO, in general the opening tempo indication of a piece is the single most important and rock-solid marking in the whole piece. Everything else revolves around that, and if something seems not to fit with it, I would say it means either that the other thing is wrong or that we're interpreting one or the other thing incorrectly.

P.S. Anyway, as you probably know, M.M's are just guidelines....

I once heard it "live" (from another student), but I cannot find it on YouTube (they seem to only have the easiest exercises in that book, which is Köhler Op.33). It is actually just an exercise, not really a piece as I had written in my OP.
It exclusively has sixteenth notes, but yes, obviously the moderato refers to the main beats you have to feel in your system, (there are 4 groups of sixteenth notes in each measure, the beamed notes being 6, not 4, that is to say sextuplets). You just have to feel those beats in your system and it will feel moderato. I could scan it, but that is actually all there is to it...

Moderato should refer to whatever is intended to be felt as the main beat, assuming the composer didn't make a mistake which of course we hope not. The main beat can feel a certain way and then have a lot of faster or slower notes added to it, but the indication is still accurate.

If it makes sense in this case, try to un-accent the majority of the sixteenth notes. If you lighten the piece up by taking away excess accents and instead letting the music flow toward the few accents that do matter, it might play faster but feel slower.

I don't understand why you say it doesn't sound moderato. It's up to the performer to convey that sense, and I don't see any obvious reason why that would be unusually difficult, as you have described the music. A steady stream of sixteenths at MM=76 seems very moderato to me, but then, all kinds of details of the score are missing from my picture - are there big angular leaps?, complicated articulations? etc. etc. - all of which affect the 'feel' of the tempo.

There are some big angular leaps, yes.
But all in all I am starting to see it as more moderato now, I am starting to get a feel for it.

there is this pianopiece with tempo indication Allegretto, which (could/should) mean: not too fast, but not sluggish, by no means extremely hurried, and yet it sounds incredibly speedy, because of it being written in 32nd notes, it's called Feux follets, by Liszt. Everything is relative...

Great example of how "tempo" indications aren't just about speed, or even mainly about speed.

They're more about feeling and spirit.