Assalaamu alaykum. In our mosque, there is an imam who watches dancing and sexual videos in that mosque. I know of it because I bought him an android phone and later came to know that he watches prohibited things on it. He also has Quran on it in audio form. How can I make "Islaah" of him. I do not have the courage to argue with an imam of the mosque. What should I do now?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

First of all, it should be noted that a Muslim must think good of his fellow Muslim brother and not accuse him of anything without evidence.

In any case, if what you mentioned is proven, then there is no doubt that it is forbidden to watch those videos, and the prohibition is more stressed if he watches them inside the mosque. Advice is part of the religion, as the Prophet informed us.

The fact that the sinner is an imaam of the mosque does not prevent from advising him, and you should not lack courage in advising him gently and wisely. Hence, we first advise you not to hesitate in advising that imaam. For benefit on someone who is embarrassed of enjoining good and forbidding evil, please refer to fatwa 137086.

There are many means by which you could advise that imaam. You may speak to him directly in a gentle, kind manner, or you could write an anonymous letter to him and deliver it to him by one way or another – without him knowing who wrote it. In this letter, you advise him to fear Allah and stay away from watching what Allah has forbidden. Or you may hang a fatwa about the prohibition of looking at what is forbidden in a place where those who enter the mosque – among whom is the imaam – may see it.

Allah knows best.