Jeremy Nixon:

There are a few things going on here, and I suspect the other replies were
about the wrong one. The most obvious is the specks of dirt all over the
place; I assume you're not asking about that because the cause is obvious.

Then there's the "texture" you get, most prominently in the T-shirt; that's
the film grain and looks fine to me. Finally, there is what looks an awful
lot like digital chroma noise, and I suspect that's what you're actually
asking about. I believe that is also simply film grain, and it's normal
(in my experience, and I'm not a Top Expert) for color film scans.

I determined to my satisfaction that it wasn't digital noise (in my own
scans) by cranking up the scanner to 16x multi-sampling, which should
eliminate any trace of digital noise, and that pattern didn't change at
all. That's just the way it looks.

Having said that, setting Color Noise Reduction to 10 in Lightroom (or
Camera Raw) will eliminate it. (Yes, you can do that on a TIFF from a
scanner.)

Thanks to everybody for their replies. I got another proof of Jeremy's
suggestion: setting a wrong focus on the scanner blurrs away the image
together with the 'noise', which turns to be how grain looks to the scanner.

Now another question:
On optical prints, even at big scales (like 1 x 1 m from 60 x 60 mm film)
there's no such noise visible. Does is mean they are printed with sifted
focus, or is it the natural blurring in the enlarger? One way to check it
would be to get my grainy scan printed in a fotolab without preprocessing.

I am not even sure this grain noise needs to be cleaned up before printing...

Anton