User accounts broken (in an odd state) since kernel panic in ML
Your first triage step is to isolate software from hardware. You could install ML clean on an external drive and see how it works or just erase your Mac and reinstall. Once you've concluded the hardware and base OS is stable, you can try the migration / restore from backup again or start narrowing down software corruption as a cause.

Assuming you can make the kernel panics happen - once you have 4 or 5, the stack trace should point to a pattern of where the system is having problems. If you can't reproduce the panic, then you may just need to clean up from a hard landing by restoring from a time before the unlucky crash.