BAGHDAD — Iraq’s president stepped in to appoint a new prime minister after the Parliament failed to do so for two months, leaving the country largely rudderless at a time of multiple political crises. The premier, Mohammed Tawfiq Allawi, is hardly a new face — he is a former member of Parliament and former minister of communications. But he is not tarnished by the corruption allegations that dog many other Iraqi political figures. In his first comments upon accepting the nomination, Mr. Allawi paid homage to the anti-government protesters who have been out on the streets since October and he...