Praise be to Allah.
Sitting in the mosque waiting for the prayer or engaging in acts of worship, is something that is prescribed in sharee’ah and for which a person will be rewarded, as the Prophet (peace and blessings of Allaah be upon him) said: “When he enters the mosque, he is in a state of prayer so long as the prayer is what is keeping him there, and the angels send blessings on any one of you so long as he remains in the place where he prayed, saying, ‘O Allaah, have mercy on him; O Allaah, forgive him; O Allaah, accept his repentance.’ So long as he does not offend anyone or break his wudoo’.” Narrated by al-Bukhaari (477) and Muslim (649).
With regard to watching television in the mosque, if it is a beneficial program that is free of haraam things, then we hope that there is nothing wrong with watching it.
But if it is a program that contains something haraam such as showing adorned women or music, etc, then the TV must be taken out of the mosque, for the mosques are the noblest of places and the most beloved to Allaah, and they must be purified of physical filth (such as najaasah and dirt) and well as intangible filth (i.e., sin).
Allaah says (interpretation of the meaning):
“In houses (mosques) which Allaah has ordered to be raised (to be cleaned, and to be honoured), in them His Name is remembered [i.e. Adhaan, Iqaamah, Salaat (prayers), invocations, recitation of the Qur’aan]. Therein glorify Him (Allaah) in the mornings and in the afternoons or the evenings”
i.e., Allaah has commanded that they be venerated, and part of that veneration is cleansing them of sin.
And the Prophet (peace and blessings of Allaah be upon him) said: “:These mosques are not for any of this urine and filth; rather they are for the remembrance of Allaah, may He be glorified and exalted, and prayer, and reading Qur’aan.” Narrated by Muslim (285).
The mosques are only built for the worship of Allaah, so they must be venerated and kept free of sin.
And Allaah knows best.