How do we apply the Sermon on the Mount today? Especially the antitheses of Matt 5:21-48?

Gustave Dore, Sermon on the Mount

Sermon on the Mount:
Personal relationships: 
"But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, 'You fool!' will be liable to the hell of fire.” (Matthew 5:21). 

Thought life and sexual ethics: “But I say to you that everyone who looks at a woman with lustful intent has already committed adultery with her in his heart” (Matthew 5:28).

Speech: But I say to you, Do not take an oath at all...Let what you say be simply 'Yes' or 'No'; anything more than this comes from evil (Matthew 5:34+37).

Attitude toward those who mistreat you: “But I say to you, Do not resist the one who is evil. But if anyone slaps you on the right cheek, turn to him the other also” (Matthew 5:39).

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• Personal relationships: "But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, 'You fool!' will be liable to the hell of fire.” (Matthew 5:21). How can we authentically worship the Creator if we have something against one of His creations, worse one of His image-bearers? If worship is truly a daily occurrence, then restoration and reconciliation with neighbors should be too. If we expect those who wrong us to make amends, then how long should we delay in making amends with those that we wrong? Sin destroyed not only our vertical relationship with God, but also our horizontal relationships with others and if the power of the gospel is penetrating all aspects of our lives then even our attitudes toward our fellow man should reflect the love of Christ.
  
• Thought life and sexual ethics: “But I say to you that everyone who looks at a woman with lustful intent has already committed adultery with her in his heart” (Matthew 5:28). How faithful are we truly being to our spouses if we fantasize about other women/men? Since purity implies perfection, then the private life of the mind is included. Though we often tell ourselves "there are things I am incapable of," we must convince ourselves that if we are capable of entertaining those things in our minds, or on our computer screens, then we stand at the precipice of a slippery slope to the commitment of the deeds themselves. Faithfulness is a black and white term (there is no such things as being “kind of faithful”), either you are or you aren't, there are no qualifications, exceptions, or allowances.
  
• Speech: But I say to you, Do not take an oath at all...Let what you say be simply 'Yes' or 'No'; anything more than this comes from evil (Matthew 5:34+37). How can we be a man/woman of integrity if we don't actually say what we  mean? What does having to “raise the stakes” so-to-speak to increase the likelihood of others  believing our words say about us? We must develop a track record of meaning what we say and saying what we mean. This goes beyond merely being honest in content, but also honest in delivery, for it is a simple matter to deceive another in the way or context of which something is said. The same goes for half-truths or “little white lies,” for Truth by definition is exclusive, yet another black and white term.
  
• Attitude toward those who mistreat you: “But I say to you, Do not resist the one who is evil. But if anyone slaps you on the right cheek, turn to him the other also” (Matthew 5:39). Why is it that our naturally tendency is to forsake forgiveness? Why do we feel the need to have the last word? To put people in their place (as we see it anyways)? Or if nothing else, gleefully await their comeuppance from God? We must remember that even The Lord's Prayer reminds us that we are forgiven in the measure that we forgive others. In this we will truly learn what it took for God to forgive us (and thus be that much more grateful!) if we also truly experience what it takes to forgive those who sin against us.