Did Moses see the face of God? Exodus 24:9-11


  9 Moses and Aaron, Nadab and Abihu, and the seventy elders of Israel
  went up 
  10 and saw the God of Israel. Under his feet was something
  like a pavement made of lapis lazuli, as bright blue as the sky. 
  11 But God did not raise his hand against these leaders of the
  Israelites; they saw God, and they ate and drank.


Here we see that Moses and others saw God with their own eyes.

But later, Moses was not allowed to see God's face.

Exodus 33:18-23


  18 Then Moses said, “Now show me your glory.”
  
  19 And the Lord said, “I will cause all my goodness to pass in front
  of you, and I will proclaim my name, the Lord, in your presence. I
  will have mercy on whom I will have mercy, and I will have compassion
  on whom I will have compassion. 20 But,” he said, “you cannot see my
  face, for no one may see me and live.”
  
  21 Then the Lord said, “There is a place near me where you may stand
  on a rock. 22 When my glory passes by, I will put you in a cleft in
  the rock and cover you with my hand until I have passed by. 23 Then I
  will remove my hand and you will see my back; but my face must not be
  seen.”


If Moses already saw the face of God, then who's face was he not allowed to see?

Who was covering Moses and preventing him from seeing God? 

Were there two people?. Or Maybe three?
The use of the word 'face' is different in these two contexts.
In the first use God is said to speak to Moses 'face to face' that is not from some distant position as in a dream, or vision but speaking audibly to him while under some visible form.  In other words, God spoke to Moses like a person does who is having a conversation.  God spoke out of a burning bush, out of a pillar of cloud, ect. and he spoke as in conversation between friends.  That is Moses could ask questions, God would answer, the conversation would continue, ect.  Speaking face to face was not the normal mode which God communicated with men, or later prophets.
Regarding the specific 'form' that God presented to the elders representing the people of Israel, it was actually a 'formless' representation of glorious fire wrapped in a cloud that made the place at which it joined the glorious upper heavens to the spot on earth which they stood, a shining clear blue. The blue a reflection of the sky of heaven. The elders saw the same thing that the people in general saw, only closer. The word 'foot' does not mean that there was some secret form, like for example the more Christlike appearance of Ezekiel 1:26 where the 'appearance of a man' was seen. The foot is meant to be understood as not a human foot but as a base. God's glory in heaven landed on earth making a covenant with his people, that was the base. Certainly if they saw a human form they would have make and idol, something which was forbidden as they had not seen any real form:

And you came near and stood at the foot of the mountain, while the mountain burned with fire to the heart of heaven, wrapped in darkness, cloud, and gloom. Then the LORD spoke to you out of the midst of the fire. You heard the sound of words, but saw no form; there was only a voice.(Duet 4:11-12)
“Therefore watch yourselves very carefully. Since you saw no form on the day that the LORD spoke to you at Horeb out of the midst of the fire, beware lest you act corruptly by making a carved image for yourselves, in the form of any figure, the likeness of male or female. (Duet 4:15-16)

The second use of the phase pertains to the manifestation of God's glory. When you look into the face of someone you can see into their eye's, along with the expression on their face, their essential personality or being.  If you only saw the back of their head, you might not even know who you were looking at.  The idea in Moses not being able to see God's face is that he could not witness the essential glory of God.  No man while veiled in sinful flesh can see God's essential unmasked glory and live:

As our bodily eye is dazzled, and its power of vision destroyed, by looking directly at the brightness of the sun, so would our whole nature be destroyed by an unveiled sight of the brilliancy of the glory of God. (Commentary of the Old Testament, Keil &amp; Delitzsch, 1.476)

Therefore although Moses wanted to penetrate deep into the glory of God he had to accept a limitation and only see the back of God.  God is using human terms to express a limited reflection of his glory.  The glory that must have appeared to him was a deep revelation of the meaning of the very words which were spoken as his 'glory passed by':

And he passed in front of Moses, proclaiming, “The Lord, the Lord, the compassionate and gracious God, slow to anger, abounding in love and faithfulness, maintaining love to thousands, and forgiving wickedness, rebellion and sin. Yet he does not leave the guilty unpunished; he punishes the children and their children for the sin of the parents to the third and fourth generation.” (Exodus 34:6-7, NIV)

It seems that part of this deeper revelation of Jehovah, the I AM that I AM, or the eternal powerful one, is by putting love and grace before wrath. However putting love first was not meant to imply that his infinite justice and wrath for sin would ever be compromised, rather his glory is simply more wrapped up in his grace and love than in his other aspects of his back-parts. Moses must have seen God's love in an extraordinary matter. Infact it made his face shine, but as the Law did not really centre in God's grace but was in a large part a revelation of his holiness, justice and wrath for sin, this glory faded and was veiled until the full manifestation of grace was revealed in the face of God's own Son. (2 Cor 3:7)
Did Moses see God face to face, i.e. see his essential glory? No, not while on this earth. However after he died, like every believer he would have immedietly become awakened into the full glory of God under the bright rays of heaven.