I have used digital distortion of different kinds a few times. I like the texture of it, but it doesn't suit every film. For instance if you're doing a classic Jane Austen Victorian movie, you probably wouldn't go there, but if you're doing a sci-fi movie, it could very well be an acceptable part of the sound design. But of course it would be both bold and fun to do it in the Victorian movie... :)
I have always loved noise in general, especially ever since my sound teacher at film school hated it, so I have tried to find good use for it whenever possible. There are many flavours of noise, from soft crackle (radio static, record scratches, optical film noise) over distortion (valves, guitar fx) techical noise (pink, white) to digital noise (jitter, bit crushers, buffer override, faulty media), and sometimes you need just a little bit of noise to bring the sound to life.
In my first feature film as supervising sound editor / sound designer / re-recording mixer, we had a scene, where it had to sound like the film itself was breaking apart. The picture was jumping all over the place, with lots of jump cuts and repeated footage, and since we were working in Dolby Digital, I thought digital errors were at its place. I used some automated bit crushing on the atmospheres, slowly decreasing the bit depth and sample rate down to around 4 bit / 1000 Hz or worse. I used buffer override on the dialogue, overlaying different errors about 10 times, as well as playing back the dialogue from a disc man while shaking it like mad to provoke errors. It was pretty extreme and loud in the end, and everybody loved it (except the so-called quality control guys, who couldn't understand it). It wasn't a science fiction film, but a pretty arty film with lots of texture to everything.
On another project, a low budget science fiction short film in black and white, I used a bit crusher in the mastering chain, bringing the sample rate down to 22 kHz and 12 bit, making everything sound like it came out of an old Akai 900 sampler. This was also pretty succesful, the director loved it, so we went with it. On 35 mm, in Dolby SR, it sounded magical!