The address on your tax return is where you want to get mail from the IRS if they have issues with this tax return.  So don't use an old address.  The address has nothing to do with whether you qualify for HOH.

I don;t know whether using the same address is an automatic audit trigger, no one really knows what the audit triggers are.  But if you are legitimately HOH because you paid more than half your housing costs for the whole year, that should be easy to prove if you are asked.