Moses' authority as spiritual leader derived from his intimate relationship and communication with God, which resulted in the divine glow on his face. This reflected glory did not last, but faded until Moses' next encounter with the LORD. Hence, the Apostle Paul noted to the Corinthian church that Moses "used to put a veil over his face so that the sons of Israel would not look intently at the end of what was fading away" (2 Cor. 3:13). In the context of Exodus we may infer that the only glory the people were to see was the reflected glory of God, not any human glory in Moses himself. And the only authority Moses had was derived from his communion with God.
By way of application, every minister of Christ today should ask himself, "Do people catch a glimpse of the glory of the Lord when I stand in the pulpit and expound His Word?" If not, what is lacking in my on communion with God?
In the Apostle Paul's analogy, though, Moses is representative of the Old Covenant. The glory of the Old Covenant, which Paul calls "the ministry of death, in letters engraved on stones" (2 Cor. 3:7), was a fading glory. It was glorious because it reflected God's holiness and righteousness; it was fading because of Israel's disobedience. God's purpose in forming a holy people of His own would be fulfilled in the New Covenant through the sacrifice of His Son and the work of the Holy Spirit in the hearts of believers. That glory, "the glory of God in the face of Christ" (2 Cor. 4:6), will not fade away.