How could Judas be appointed to preach the Gospel?
In Matthew 10:1 is written: "And when he had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease." And in verse 4: "and Judas Iscariot, who also betrayed him." How is that possible? Judas got an appointment to preach the gospel?
The reason that God gave his twelve disciples this authority to preach and even do miracles had nothing to do with the persons themselves. It was to give testimony to the claim of Jesus to be the Messiah and to introduce Him and His message to the people. In other words, they were His instruments to advance God's Kingdom in and through His Son Jesus Christ. God has often used various instruments. Often people that were very wicked. Think of the Babylonians and Assyrians. In Ps. 17:13 David calls the "wicked, which is thy sword." He even used the Jews to fulfill His hidden will. Peter said in Acts 4:27-28, "For of a truth against thy holy child Jesus ... the people of Israel were gathered together, for to do whatsoever thy hand and thy counsel determined before to be done." In the OT He even used Balaam to make some beautiful prophecies of the coming Messiah.
So back to Judas Iscariot, God used Him in His service even though He knew that although Judas Iscariot began to follow Him, he eventually would betray Him. In John 6:70 Jesus even said, "Have not I chosen you twelve, and one of you is a devil?" At first Judas Iscariot was undoubtedly sincere about his intentions to follow Jesus. His understanding of Jesus Christ was, however, completely earthly. In all fairness, the other disciples also did have this expectation at first as most of all the Jews did. But throughout the years of Jesus' ministry, Judas more and more hooked off. Jesus' kingdom was not the kind he desired. This caused a great anger and hatred within Judas' heart. It led finally to his act of revenge in which he betrayed the Lord Jesus.
Did Jesus then make a mistake in allowing Judas to be His preacher and even sending him out with the others to preach the Gospel? Or did the Lord Jesus send him purposely even though He knew that Judas was fake? Perhaps neither one is correct. I think the Lord Jesus sought Judas' repentance all along. Throughout the three years, in which Jesus knew the inner motive and thoughts of Judas, He never gave a single clue about what He knew Judas was all about. He showed him the same genuine love and care that He showed to the others. Judas received all the teachings and sermons the others did receive. He even entrusted Judas with the bag of money as the treasurer. Till the end He continued to heap coals of fire on Judas' head to seek his repentance. When finally Jesus announced that 'one of you is going to betray Me,' nobody concluded immediately, "Oh, that will be Judas Iscariot." They had no clue it was him but neither had the Lord ever given a clue in His dealings with Judas what He knew about him. Would you act the same to one of your 'friends' when you knew he was setting the net to kill you?
So to sum up, Jesus wasn't at fault that the preacher He sent out wasn't sincere. Judas had come and joined himself to Jesus. When Judas preached, he would have preached the truth, "Repent ye and believe, for the Kingdom of heaven is near." We may assume that he also did miracles.
Paul wrote about 'preachers who also didn't preach Christ out of the right motives. In Phil. 1:15-17 he refers to believers who were preaching from selfish ambition, envy and strife. But notice that Paul rejoiced nonetheless. Why? Because the teachings of Christ were spread around and that's what rejoiced Paul.
For certain, Judas wasn't a believer and therefore this passage doesn't completely apply to him. Still, he was used by God and what how much he had to answer for, when finally he hastened himself through suicide before the judgment seat of Jesus Christ.