These days dithering is a lost technique other than as an arty effect. It's a shame, digital video playback would really benefit from it as a way to eliminate posterization.
The dithering techniques like Floyd Steinberg and Atkinson taking 8 or 4 bits per channel down to 1 bit per channel are definitely anachronistic, but not dithering where the goal is 8 bits per channel.
I’ve made very expensive mistakes printing poster-sized art without using dithering, and you can end up with visible color-banding in gradients in the print that aren’t visible on a display. This is why we still need and still have dithering. This is the reason that Photoshop quietly dithers by default when you convert from 16 or 32 bits per channel down to 8 bits per channel.
There appears to be active research on new dithering techniques. I ran across libdither [1] which implements more dithering algorithms that you can imagine.
I have noticed that if you get up close to the surface of a car in a lot of modern racing games it has a very noisy/sparkly shader. I know some paint does look like this, but I always suspected this was to prevent banding by creating sub-pixel noise.