"Now when Ezra had prayed, and when he had confessed, weeping and casting himself down before the house of God..."

Ezra 10:1
Ezra knew that there was a problem.  Ezra 9:1 says, "...The people of Israel, and the priests, and the Levites, have not separated themselves from the people of the lands."  Notice the order.
First, the People - "For all have sinned and fallen short of the kingdom of God."  There is no one who is exempt.  The entire nation have failed to keep themselves separate.  They had married people of other lands; just look at the list of them - "Canaanites, Hittites, Perizzites, Jebusites, Ammonites, Moabites, Egyptians and the Amorites."  (Ezra 9:1).  Most of this list of peoples were involved at the time of Joshua.  God had called the Israelites to destroy these evil nations.  The fact that these nations had again infected the Holy Nation of Israel is testament to their disobedience.  The Christian life can be like this, for in our lives we are to turn away from our previous life.  There should be a change in us that is evident.
Next we have the priests, those who served God in the place of His choosing.  These people should have known better, but had also chosen wives of people that God specifically demanded that they shouldn't.
Finally, we have the Levites.  These were those who had set themselves apart for God when Moses called for those who would deliver the judgement of God.  Indeed, they exacted the death of their brethren for this very crime (Exodus 32:25-35 tells us the full story of the Golden Calf).
When Ezra was told about this problem, he immediately began to pray.  His prayer is recorded in Chapter 9.  His attitude to the sin is what intrigues me.  He was told and he begins to pray.  He confesses everything to God, while he wept.  He wept outside the house of God - outside the place where God was.  He felt He was unworthy to go inside and pray for the people.