Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is permissible and there is no objection to playing these videos inside the mosque as long as they are screened outside the obligatory prayers’ timings and provide beneficial material to the congregation.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
In Islam, the mosque is one of the basic institutions that plays a major role in promoting truth, justice, knowledge, and goodness within the community. As places of congregation, mosques provide Muslims with regular opportunities of acquiring knowledge and engaging in a unique social platform.
These are the fundamentals upon which the Prophet Muhammad (peace be upon him) established his mosque when he came to Medinah.
Back in the early days of Islam, the mosque presented numerous important functions that included, but were not limited to, social gatherings, educational classes, court sessions, hospital, house of treasury etc.
The mosque was part and parcel of the Muslim community’s fabric. Lady ‘Aishah (may God be pleased with her) narrated that the Prophet (peace be upon him) said, “Publicize these marriages, conduct them in mosques, and beat the duff (tambourines) to announce them” (At-Tirmidhi)
To promote Islam and serve da`wah purposes, the Prophet (peace be upon him) used to receive delegations of different faiths in his mosque. For instance, he received Najran’s Christian delegation and others in his mosque for mutual discussions and interactions.
The Prophet’s biography is replete with examples that attest to the role the mosque plays in the society.
Though it is considered a big institution in Islam, the role of present-day mosques is restricted to observing regular rituals such as prayers, Quran recitation, and itikaf (spiritual retreat).
This, in turn, has led to confusion with respect to the things that mosques could offer to Muslims other than the established rituals.
Consequently, there is no harm in using modern devices inside the mosque with the purpose of educating or raising people’s awareness on certain values or matters. It is established that whatever is in the best interest of Muslims is deemed permissible, provided it is used within the etiquettes prescribed in the Shari`ah. The Prophet (peace be upon him) started a small school in his mosque where he, along with the Companions, conducted lectures on Quran and the ethical values of Islam.
Based on the above and in reference to the question, it is permissible and there is no objection to playing these videos inside the mosque as long as they are screened outside the obligatory prayers’ timings and provide beneficial material to the congregation.
Almighty Allah knows best.
Source: http://www.dar-alifta.org/Foreign/ViewFatwa.aspx?ID=10512