One of the first things that always comes to mind is how salvation by God's free grace radically affects how we treat unbelievers or skeptics. When we truly understand the biblical gospel of the grace of God in Christ it removes the "us vs. them" mentality. If it teaches us anything, being saved by grace alone teaches us that we are no better than anyone... that we are all desperately cracked about the head ... and so when we see great evil in the world we do not say "oh look at them...we are better"... no, we say "but for the grace of God there I go". .. and I think this goes a long way in helping begin to repair the problems between people in the world ... and enables us to have a point of commonality with others .... we then see others as fellow human beings who are sinners like us, with the same struggles we have. We become overwhelmed by a sense that since such enormous free forgiveness has been extended to us, how could we not extend a forgiveness to others? If God granted us unconditional grace, then we find the strength to extend such grace to others, even and especially those who are our active enemies.
And when, by the grace of God, we engage in good works, grace teaches us that we cannot boast in them or compare ourselves with "those bad people out there" but see our doing good as part of the overflow of God's grace to us, giving rise to a thankful heart ... and so if we understand grace correctly, it leaves us no room for boasting over anyone. Rather it interact with others who differ from us with humility. These are some horizontal applications.