Let me say first that I thoroughly enjoyed his book. But as powerful as it was, it was not his book that gave my family a new perspective on our service to Jesus. His book directed me back to Scripture and the amazingly difficult statements Jesus said to his followers. Here's a good video that advertises the book:
The message here is spot on! But my problem with "radical Christianity," "radical obedience to Jesus," & "radical living" is that the Bible never uses the term "radical" in such a way. Granted, Jesus' words to his disciples to give up everything, take up their cross, love Jesus more than anything else (a seeming hatred for family and friends almost), and follow Jesus are quite radical. But the Bible simply calls this obedience not "radical obedience."
To add the adjective "radical" is more or less a statement on American Evangelical Christianity. In other words, how we have perceived and practiced the faith has very little to parallel it with the command of Jesus for his disciples to follow him. Thus, when we are given these truths, we are shocked into a reality (many never "counted the cost" to follow Jesus in the first place) that says, "Wow! I didn't know this. My obedience to Jesus needs to be more... radical!" All along, however, obedience to Jesus has always been the same. Platt (and others like Chan, Washer, and Black) are not rediscovering truths from the Bible. They are simply pointing out what has been lacking in American Evangelicalism - a gospel of repentance and discipleship: Jesus' gospel.
Christianity is only "radical" when we practice a soft form of it, which is not really the Christianity Jesus professed to begin with. Following Jesus is simply obedience. It is radical in terms of what it costs and the way the world will perceive it. But within the realm of the Way, there is not multiple levels of obedience - bad, good, and radically great. There is simply obedience. You either obey Jesus by giving him yourself, your family, your friends, your life, your possession, and follow him. Or you reject him out right or through reservation (a "comfortable christian"). Yes... live radically! But understand the Bible calls that obedience. Anything less is not the gospel.