Random screen captures in Galaxy Tab 10.1
What have you done after the factory reset -- installing everything you've had installed before? Best way to figure out where the problem is located is:


Backup as much as you can
factory-reset the device
do not yet install/restore anything!
check for a reasonable time whether the problem re-appears

if it does right after the factory-reset, your device needs go to support (or they need to send a firmware update/fix)
if it not re-appears, continue with 5.
if it does re-appear, you've found the app causing the issue. Break here, see below.

re-install/recover ONE app. Repeat from 4.


If above steps resulted in an app being the cause, you've got multiple choices:


re-configure the app and see if you can make the error go away
uninstall the app and see if the problem goes away
if none of the two works, start with step 2. above and skip the bad app.