Office of Grand Ayatollah Khamenei (may Allah grant him long life):

Justice (adalah) means that quality of the inner spirit with which a man can abstain from carnal desires and can develop a command over the correct performance of compulsory acts. In other words it is the state of fear of God which always permeates the just man's mind. To make sure whether a person is just or not, the goodness of appearance of the individual is sufficient. According to a strong opinion, it is permissible for one who considers himself as lacking 'adalah' (the quality of justice) but the followers (mamumeen) believe in him as being just, to act as a prayer leader, although the precaution for him is not to do so. However, the congregational prayer is in order and the rules concerning Jama'at (congregational) prayer apply to it. Therefore, the rules regarding the quality of justice characteristic of congregational and Friday prayers do not make any difference.

Office of Grand Ayatollah Sistani (may Allah grant him long life):

It does not make any difference.

Office of Grand Ayatollah Makarem Shirazi (may Allah grant him long life):

It is necessary for Friday and congregational prayer leaders, Hākim Shar'a (qualified Muslim ruler) and Mujtahid to be just (adil), and there are different ways to prove the quality of justice. For example, there is a prayer leader leading prayers in the famous mosque of the city with apparently pious people following him. This much is sufficient to prove that he is just. As for the Friday prayer leaders, we know that they are not appointed as Friday prayer leaders unless complete investigation has been made about them. Adalah is the state of fear of God which always permeates the just man's mind and which prevents him from committing major sins and repeating minor ones. If a person associates with someone and does not see him commit sins, it is a sign of him being just; this is called 'goodness of the appearance' which is an indication of the quality of the inner spirit (or secondary habit ingrained in him).

 Office of Grand Ayatollah Saafi Gulpaigani (may Allah grant him long life):

There is no difference between them in terms of justice.