Remember the Sermon on the Mount is not a new set of laws and regulations -- it is evidence that our hearts have been (and are continuing to be) transformed by the reality of the arrival of the Kingdom of the Heavens!
When my heart is transformed by the power and love of God through Jesus Christ, I no longer have the burden of comparing my deeds to others and my failings to others. In a word, I can surrender dismissals, put downs and looking down at others' behavior. I am free from spiritual competition and pride that requires me to drag those doing better down to my level and making sure those below me never get up to where I perceive myself to be. Nothing kills a community faster than self righteous and judgmental Christians. The Church is not a museum of Saints nor is it a gathering of the perfected. It is a hospital for sinners and we are all in the intensive care ward.
The lessons on prayer in seven are all lessons in persistence -- keep asking, keep seeking, keep knocking. I believe that in persistent prayer we should pray until either God clearly answers our prayer or God changes our prayer -- that is when God tells us that what we are praying for is not going to happen we will adjust our request out of relationship and obedience and pray for the new thing God has revealed.
The point of chapters 5-7 is spelled out in verse 15-20. Good trees bear good fruit. Bad trees bear bad fruit. The point of the Kingdom of the Heavens is that we are being transformed by neutral or bad into good. It is an internal process and is fundamentally a matter of the heart. If my heart is right than good things proceed from my heart. If my heart is bad -- all that I touch and do will also be bad. To put it another way -- verse 24 and following -- we must not just hear what Jesus is saying we must follow through. We must apply the teaching and relationship to our day to day journey and be transformed into the Sons and Daughters God created us to be.