Dwight L. Moody (1837—1899) was born into a large poor family in a small town of Massachusetts, and moved to Boston when he was 17 to sell shoes and find fortune, but found Jesus instead, and become one of the most influential and famous revivalist preachers in American history, and almost all American Evangelicals have somehow been influenced by him directly or indirectly. Arguably, millions are Christians today due to Moody's missionary work. I was once a member of Moody Church when I lived in Chicago in a high-rise apartment that overlooked Moody Bible Institute, and own several books printed by Moody Publishers. D. L. Moody has left an impressive legacy that is still going strong after almost 200 years, a feat paralleled by few to none.
An Introduction to D.L. Moody
In an ironic way, D.L. Moody's pursuit of fortune lead him into a missionary work to help the poor and to become a Christian evangelist. Moody moved to Boston to work in his uncle's shoe store, aspiring to build a fortune of $100,000. His uncle hired Moody under the condition that he would attend church. On April 21, 1855, Moody was converted to Christianity when his Sunday school teacher, Edward Kimbal, visited him at work, and compelled him to accept Christianity. Moody's conversion experience became a centerpiece of his later Revivalism, where preachers made appeals to people to make a decision to accept the Gospel at that very moment.
Moody left his uncle's shoe shop at the age of 19 to become a businessmen in Chicago. Moody had compassion on the poor, and purchased seats at churches (because seats were sold like concert seats today), so the poorest children could attend church. The Church congregations didn't like the rowdy children that Moody brought, so after failed attempts to include poor children into churches, Moody established his own Christian Sunday School. Crazy Moody's mission work gained the attention of Abraham Lincoln, who visited Moody's School, and changed Crazy Moody's reputation, such that people called him Brother Moody thereafter. There's far more to Moody's story that I wish to discuss here and now, yet it's not an exaggeration to say that Moody's influence and fame stretched worldwide even to this day. Moody is arguably one of the greatest Revivalist preachers the world has ever known (here's an audio recording of Moody's voice). 
Karl Barth's criticism of D. L. Moody
Moody was world famous, but not everyone was a fan of Moody's approach to ministry. In Karl Barth's Table Talk, I discovered the following criticism of D.L. Moody.
Student: What do you think about preaching for decisions in Revivals?
Karl Barth: That is a question of pedagogy, tact, psychology, and of the concrete situation. I do not like it as a system of evangelisation. I do not pronounce a prohibition to extraordinary men like [Dwight L.] Moody, who can do what cannot generally be done. All methods are problematic. As a venture, yes. Exclude appeals and you have an ecclesiastical fortress: preaching, prayer, worship. Some want to come out of the fortress and fight. The Apostles did not ask people whether they would accept or not, but told them of reality, not in a sense of false freedom but of true freedom. Concentrate on teaching and preaching the Word of God, and let experience take care of itself. And what I say in the Church Dogmatics is not something to preach. These volumes are for your study. When you go into the pulpit, go with the Bible and the Holy Spirit! 
Explanation of Barth's Criticism of MoodyKarl Barth wasn't a fan of Revivalism, and revivalist preachers like D.L. Moody, because he believed Revivalism was a questionable way to do evangelism. In Revivalism, itinerate preachers would speak to large crowds, and asked people to immediately accept the Gospel, at that very moment. Barth was concerned that this was a form of psychological manipulation, that was not a proper way to teach Gospel, and he also believed Revivalism wasn't tactful—some revivalist preachers were animated entertainers (similar to circus performers) and would draw large crowds due to their antics, such as Billy Sunday. Barth also dislikes the fortress mentality of Revivalism, where preachers built enclaves, from which they would come out to fight the world.
The Gospel doesn't require us to accept it
Karl Barth's primary criticism of Revivalism in general and D.L. Moody in particular, was that the Apostles did not ask anyone to accept the Gospel, because the Gospel didn't depend on anyone accepting it. The Apostles proclaimed the Gospel, whether people accepted it or not! So Barth rejected Moody's Revivalism, because it changed the Gospel from proclamation of the good news of Jesus Christ, into a conditional limited time offer, that one must accept right now, before it is too late!
Barth said that the conditional Gospel of Revivalism, gave people a false sense of freedom, or assurance of their salvation, that was brought about by their personal decision. Barth said this false freedom is not the true freedom of the Gospel, and is a false reality. The true reality is that the Gospel proclaims the good news of Jesus Christ to the whole world, not just those who respond. Barth's criticism of Revivalism is of key importance even today, because it is still common to hear preachers ask people to "ask Jesus into your hearts" or "receiving Christ into your heart" or "pray the Sinners prayer" or preform "alter calls" and other forms of call to action to obtain an immediate response. Barth believed we may respond to the Gospel in thankfulness, but the Gospel is not conditional upon our acceptance of it. (In essence, this is problem with all forms of semi-Pelagianism as such.)
Karl Barth on Moody specifically
Barth names Moody specifically, when asked about Revivalism in general. Moody's fame had stretched worldwide, and Barth had learned about him from across the Atlantic Ocean. Barth didn't wish to stop Moody's ministry, or to undermine Moody's success. Barth says all methods are problematic, but not all are equally problematic. Barth acknowledged that Moody had made an impressive accomplishment, but Barth did not think that others should imitate Moody. Moody is an extraordinary exception, and there is only one Moody, and Barth was impressed by Moody's successful venture into Revivalism.
Concluding Remarks on Barth and Moody
In nuce, Karl Barth desired that all appeals be removed from preaching the Gospel. The preacher preaches with their Bible and by the Holy Spirit, and the Gospel is proclaimed to the entire world, regardless of whether the world accepts it or not, because it is not a limited time offer or conditional upon any person's decision for Christ. Barth says that Church Dogmatics are helpful to preachers in their private studies, but Barth opposes fortress mentality or enclavism, where the preachers hide from the world, and then come out of their fortresses to fight. Karl Barth admires the accomplishments of D.L. Moody, but Barth believes that Moody should not be made into a pattern for others to imitate.
Moody Church recently celebrated their 150 year anniversary, and has much more information on the history of D.L. Moody and his ministries.
[^Header Image] Dwight L. Moody: The Man and His Mission. Chicago: Monarch Book, 1900. Print. [Header images and historical information on D.L. Moody]
[^1]Severance, Diane, and Dan Graves. "Dwight L. Moody Was Converted." Christianity.com. Christianity Today, June 2007. Web. 21 Apr. 2017. <http://www.christianity.com/church/church-history/timeline/1801-1900/dwight-l-moody-was-converted-11630499.html>.
[^2]"The Moody Church." A Brief History of The Moody Church | The Moody Church | Chicago, Illinois. Moody Church, n.d. Web. 21 Apr. 2017. <http://www.moodychurch.org/150th-anniversary/brief-history-moody-church/>.
[^3] Barth, Karl. Karl Barth's Table Talk. Ed. John D. Godsey. London: Oliver and Boyd, 1965. 38. Print.
[^4] By BPL - originally posted to Flickr as Preaching, CC BY 2.0, Link
Related: Church Dogmatics, D. L. Moody, Dwight L. Moody, Karl Barth, Moody, Revivalism, Table Talk, The Moody Church