What flash are you using with the camera? It looks kind of like a Vivitar 283, but I cannot be sure from the image.
Some older flashes dump the entire charge through the camera. This can damage some cameras, others protect against the full-current discharge.
Shoot some pictures without the flash. Sometimes- induced current finds it's way into digital electronics and has an affect on processing. Looking at the JPEG images, it looks like the image is corrupt- as in bits in the pixels either being stuck, or being dropped.
Seeing as the flash is visible in the image I'm going make the wild assumption that the flash was fired remotely.
I would like to see a remote flash frying up a camera because of full-current discharge.
This looks like a mighty fine in-camera processing problem to me.
Seeing as this doesn't happen with RAW I'd suspect the in-camera JPG processing.
This pattern repeats itself every 8 pixels, that's one heck of a nice computer number for ya (2 to the power of 3, also happens to be the length of one bit).
Have you tried adjusting the JPG quality to see what happens? It might be that adjusting the quality causes the processing to skip a process or do it differently which could make the problem disappear.
If that doesn't help you could also try to upgrade the firmware... If there's a software problem somewhere it might be fixed that way.
I'll ask my dad if he has an idea tomorrow, his job is hard-core image processing (like automatically analyzing security-camera footage kind of processing). He might just have some more ideas.
However, if a firmware update won't work I'm thinking this might be a problem you can't fix which would mean sending it back to Nikon for repairs or replacement.