Praise be to Jesus and Mary, now and forever.  
Jesus chose the Apostles after a night spent in prayer.  
St. Luke, in his Gospel, particularly emphasizes Christ's prayer, and he's the only one who informs us that Jesus spent the whole night in prayer before choosing the Apostles.  
Because He is God, Christ always knew whom He would choose.  
So He was not praying for light to see who the right people to choose were, as we must do.  
He probably prayed for the Apostles to correspond well to their vocation, for it to bear fruit.  
And in fact, almost all of them became saints.  
There's only one well-known exception: Judas Iscariot, who betrayed Him and, in his despair, committed suicide.  
This shows us that God's grace always requires our correspondence.  
No one is saved except by cooperating with grace.  
Jesus knew how Judas would wind up, and yet He still chose him.  
He gave him a chance, even though He knew that he would fail in the end.  
He gave him all the help necessary to succeed.  
He treated Judas like a friend to the end.  
Thus, Judas becomes a cautionary tale, so that no one will presume to be saved without a serious effort to correspond to God's grace.  
We can draw other lessons from the choice of Judas.  
St. Ambrose comments: How great is the truth that not even a hostile minister weakens.  Christ works even through unfaithful ministers.  Judas was sent out with the other eleven to preach the kingdom of God, heal the sick, and drive out demons, and doubtless he did so.  
St. Ambrose also points out that our Lord, who had assumed the cruelty of man, was willing to be forsaken, was willing to be betrayed, was willing to be handed over by His apostle.  He did this so that you, when abandoned by an ally, betrayed by an ally, might bear with moderation that your judgment is heard, that your kindness has been wasted.  
After Christ chose the Apostles on the mountain, He came down with them and stood on a stretch of level ground.  Here, He will preach what has been called the Sermon on the Plain, St. Luke's version of the Sermon on the Mount.  But before He does that, He has the opportunity to present His newly chosen Apostles.  
St. Cyril of Alexandria wants us to observe that their appointment was not done in a corner and secretly, but rather when many disciples were gathered together and a vast crowd from all the country of the Jews and from the seacoast of Tyre and Sidon.  This is important.  The Church Christ was founding is a visible and public institution, and so the leaders of it need to be visibly appointed, need to be appointed in the sight of the people.  
In the words of the Second Vatican Council, the Apostles were both the seeds of the new Israel and the beginning of the sacred hierarchy.  And so Christ presents the future leaders of the Church to a great crowd of His disciples and a large number of both Jews and Gentiles, since the Church will be made up of both of these two peoples who come together in one, united in Christ.  
Before He begins His sermon, He demonstrates His power and authority by healing the sick and driving out demons.  And in this way, He also makes the people more ready to hear His words.  His power and authority are divine, and this gives weight both to the words that He will speak in His sermon and to the appointment of the Apostles.  
When He later sends out the Apostles to preach, people will see that they have the same power.  They too can heal the sick. They too can drive out demons.  They too preach with authority the kingdom.  
Yet, even though Christ has divine power, He still meets us where we are.  St. Ambrose points out the moral significance of the fact that Christ ascended the mountain with His Apostles and then descended to the crowds.  How would a crowd see Christ, says St. Ambrose?  How would a crowd see Christ except at a low level?  It does not follow Him to the heights. It does not climb to majestic places.  So, when He descends, He finds the weak, for the weak cannot be high up.  
St. Matthew likewise teaches that the weak were found or were healed after Christ had descended from the mount, after the Sermon on the Mount, in his case.  We are weak and wounded by sin, and therefore we cannot mount to the heights of virtue.  And so, St. Ambrose explains, first each was healed, so that little by little, with increasing virtue, he could ascend to the mountain.  
On the plain, He heals each, that is, He calls them back from recklessness.  He turns them away from the harm of blindness.  He descends to heal our wounds, so that in an effective and abundant manner, He makes us partakers in His heavenly nature.  
To be healed, we must come to Jesus.  But there is power in Him to heal each one of us.  St. Luke says, everyone in the crowd sought to touch Him, because power came forth from Him and healed them all.  He is the source of all healing. We must come into contact with Him.  And mysteriously, this is best done by going through Mary.  
In the first reading, we heard the Corinthians were not going to Jesus as they should have.  St. John Chrysostom says St. Paul could be pointing out as many as four problems.  The first is not knowing how to bear being wronged.  The second is to do wrong.  The third is to reserve settlement of the matter to the unrighteous.  And the fourth is that this kind of thing is being done to a fellow believer.  
A Christian should imitate Christ, who did not shrink from being betrayed, did not shrink from being harmed.  The more perfect thing is to suffer wrongs for love of Christ.  St. Peter says, when He was reviled, He did not revile in return.  When He suffered, He did not threaten, but continued entrusting Himself to Him who judges justly.  But the Corinthians were returning wrong for wrong, and many do the same today.  This is not just imperfect, it is sinful.  
You can defend your rights, and sometimes it's even obligatory, namely when someone else's good is at stake.  But when you choose this route, it is best to resolve the dispute among Christians, rather than seek justice from the unrighteous.  
In the early centuries of the Church, Christians went especially to their bishops to have them settle disputes.  Bishops are the successors of the Apostles, so they have authority from Christ to judge.  St. Augustine talks about judging such cases.  
With time, the whole society became Christian, so the regularly appointed judges were Catholic, and going to them no longer meant seeking justice outside the Church.  Thus, the custom of having the bishop judge disputes fell out of use.  
Today's Western society is ever less Christian, but on the other hand, bishops are very busy, so they probably don't want people knocking on their door to have them judge their disputes.  Perhaps a reasonable alternative would be binding arbitration, with an arbiter competent in law and known as a good Catholic.  
Whatever we do, let us be guided by the example of Christ and of His saints.  
Praise be to Jesus and Mary, now and forever.