What are some problems with non-Reformed views of the Sermon on the Mount and how does the Reformed view avoid (or answer) those same problems?
Sermon on the Mount presented enormous challenge to Christians to follow on the surface. Jesus basically went beyond the OT Torah Moses laws, as given to Israel. Like you shall not commit adultery, but Jesus said if you look at a woman with lust, you have committed adultery. Like an eye for an eye in the OT, but Jesus changed it to if you are slapped on the left cheek, turn the other cheek too.
Anabaptists seeing the radical nature of the call of Jesus on SM, decided to withdraw from the society and the civil law in order to really live out the commands of SM.
Thomas Aquinas taught in his Summa Theologia there are two levels, one is for all Christians, and a second for application only to a few, and that’s his way of separating the laity and clergyman as the commands are too hard for the former, which is essentially what the Catholics have taken.
Reformed teaching is saying not to turn SM into a new legalism with the stringent application of all the details, but the discovery of a new, radical love for both God and neighbor in our hearts. Jesus said in a number of places that he is the fulfillment of the law. That’s the only way to approach SM, by knowing and expediting the radical love of Jesus in our hearts, we can, and only then, respond in l=kind with our love to him and gradually our neighbor.
I think SM reaffirms the OT laws and point to Jesus as the ultimate fulfillment of the OT law. And we will have greater respect and understanding on the relationship between OT law and NT grace period in Christ.