Status of the imam in Islam
Question

Is it appropriate for a paid Imam to be the director of the Masjid at the same time? In other word, conflict of interest, please explain.
Praise be to Allah.There is no reason why the imam should not be the director of the mosque at the same time, even if he gets a monthly salary. The imam of the mosque is the one who is responsible for the mosque; his role is not restricted only to leading the prayers, because the imaam in the mosque is like the sultan in his sultanate – unless he cannot manage the mosque properly or he is too busy and cannot take care of all the things he needs to, in which case there is no reason why another man should not be appointed to take care of mosque administration, so long as that is with the imaam’s agreement. Or duties may be shared among some of the worshippers. 
Leadership (imaamah) in Islam.
Note, may Allaah bless you, that the position of leadership is a divinely ordained system through which Allaah gives us practical guidelines to achieve noble aims and lofty purposes, such as worshipping Him well and following the leaders in cases of jihad. Hence the Sunnah of the Prophet (peace and blessings of Allaah be upon him) and the way of all the Rightly-Guided khaleefahs and those Umawi (Umayyad) and ‘Abbaasi (Abassid) rulers who followed their path was that the leader would also be an imam or leader of prayers and of jihad. Whenever the Prophet (peace and blessings of Allaah be upon him) sent a commander in war, he would lead the prayers too, and if he appointed a man as a governor over a city – as when he appointed ‘Ataab ibn Usayd (may Allaah be pleased with him) to govern Makkah and ‘Uthmaan ibn Abi’l-‘Aas (may Allaah be pleased with him) to govern al-Taa’if, and ‘Ali and Mu’aadh and Abu Moosa (may Allaah be pleased with them) to govern Yemen, and ‘Amr ibn Hazm (may Allaah be pleased with him) to govern Najraan – the person whom he (peace and blessings of Allaah be upon him) appointed would lead them in prayers and carry out hudood punishments amongst them. This was also the practice of the khulafa’ who came after him and those who succeeded them, namely the Umawis and some of the ‘Abbasis, because the most important matters of religion are prayer and jihad. 
With regard to the imam’s role in society, there is no doubt that it is an important role. How can it be otherwise when he is leading the prayers which are the most important pillar of Islam after the Shahaadatayn (twin testimony of faith)? The imam is the leader and the worshippers behind him are his followers. The imam guides and leads his jamaa’ah (group) by giving lessons and talks. The Messenger of Allaah (peace and blessings of Allaah be upon him) and the Rightly-Guided khaleefahs used to hold gatherings in the mosques where the Muslims would gather so that they might consult with one another concerning religious and worldly matters and so that they might teach the people about Tawheed, fiqh, good manners, and also enjoin what is good and forbid what is evil.” 
See Ahkaam al-Imaamah wa’l-I’timaam fi’l-Salaah by al-Muneef, p. 64 
The imam should check up on those who are absent (from the prayers), and visit the sick, He should strive to meet the needs of the Muslims who pray with him, teaching the ignorant, admonishing the negligent, advising the erring, reconciling those among whom there are differences, bringing them closer to one another and striving to foster friendship and love between them. He should strive to solve social problems that arise among them such as family quarrels, disputes between neighbours and the like. To sum up, the role of the imam is very important and should be appreciated as such. The group should help him to achieve the aims of sharee’ah and ward off anything that is bad or harmful. And Allaah is the Source of strength.