...4) To recover damages or to secure equitable or other relief under any Act of Congress providing for the protection of civil rights, including the right to vote.
This was interesting.
Problem is no precedent for quo warranto against sitting US president in any district court and the DC court is the one with the best prospects, not the Third or any other non-DC circuit court. Judge Carter said as much. The Third Circuit can easily punt the quo wararnto part of this case, and I expect that they will.
Regarding failure to verify original BC and NBC status, I don't see a remedy available to the courts under separation of powers, now that Obama has been inaugurated.