Is it permissible for an Imam, who receives a salary, to also be the director of the mosque at the same time, and does this represent a conflict of interest?

There is no objection to the Imam of the mosque being its manager, even if he receives a salary, for the Imam is responsible for the mosque and his role is not limited to leading prayers. He is like a ruler in his domain.

The status of Imamate in Islam is great; it is a divine system for teaching obedience and following leaders. The Prophet (peace be upon him) and his Rightly Guided Caliphs made the mosque a center for Muslims to gather for consultation, and to teach them Tawhid (monotheism), Fiqh (jurisprudence), and morals, as well as enjoining good and forbidding evil.

The Imam's role in society is important; he is a leader for the worshippers, guiding and directing them through lessons and sermons. He also checks on the absent, visits the sick, strives to fulfill the needs of Muslims, teaches the ignorant among them, warns the heedless, advises those who err, reconciles disputes among them, and works to bring them closer and spread affection and love among them. He also tries to mend social rifts, such as family disputes and neighborhood quarrels.

The Imam's role is great, and he must appreciate it to its full extent. The community, in turn, must assist him in achieving legitimate benefits and warding off evils and harms.