iPad screen goes foggy intermittently

I Also, still believe that it is a hardware issue, but if you really want to rule out software issues, restore the iOS software using iTunes. Backup, restore the iOS, then restore the backup. If the problem persists, restore as new and see if it goes away then. You can add your content back manually.

IF that fails, you can pretty much assume that it is hardware.

Tossing in my opinion that it's a hardware issue, likely the digitizer. Please feel free to keep trying the restore or reset, but honestly if it persists, you paid too much for the device to have to deal with glitches. ANd if it is hardware it's just a matter of time before it fails totally. ANd if that screen dies you can't enter a passcode to get it backed up. If it were mine I would still take it in to be checked, if for nothing else than to official document that your device has a problem.

Make an appointment at an Apple Store and let them take a look at the iPad.

I Had this on a mini 3, I tried everything, even a backup and restore. Multiple responses were a new lcd screen was needed.

I would schedule the appointment. For me it also looks like hardware issue. It does not matter if it hapens ocasionally or all the time. Do not underestimate display issues.