When was Acts written? We know that Acts was written by the same person who wrote Luke. Since Luke-Acts is dependent on the works of Josephus, it had to be written after 100 AD. Since Luke is addressed to Theophilus (Luke 1:3) who was made Bishop of Antioch about 170 AD, this is the most likely date of composition. This is much later than the traditional dating of 80-130 AD, however as there is no solid evidence that Acts was written before this time, this later date is just as likely, if not more likely than the traditional dating.
While Galatians was likely written approximately 130 AD, the earliest existing copy of it (Papyrus 46) is from about 200 AD, so it's entirely likely the first two chapters were added on in the intervening decades.
According to Acts, after Saul (later known as Paul) received his vision, he was struck blind and had to be healed by Ananias:
So Ananias departed and entered the house, and after laying his hands on him said, "Brother Saul, the Lord Jesus, who appeared to you on the road by which you were coming, has sent me so that you may regain your sight and be filled with the Holy Spirit." And immediately there fell from his eyes something like scales, and he regained his sight, and he got up and was baptized; and he took food and was strengthened. Now for several days he was with the disciples who were at Damascus (Acts 9:17-19)
This implies that Paul learned about Christ from the disciples. Paul disagrees:
For I would have you know, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but I received it through a revelation of Jesus Christ. (Galatians 1:11-12)
According to Acts, God wasn't too pleased with Paul:
For I will show him how much he must suffer for My name's sake. (Acts 9:16)
Galatians gives us a different view:
But when God, who had set me apart even from my mother's womb and called me through His grace, was pleased to reveal His Son in me so that I might preach Him among the Gentiles (Galatians 1:15-16)
Did Paul go to Jerusalem right after he was converted? Acts and Galatians once again differ:
When he came to Jerusalem, he was trying to associate with the disciples; but they were all afraid of him, not believing that he was a disciple. But Barnabas took hold of him and brought him to the apostles and described to them how he had seen the Lord on the road, and that He had talked to him, and how at Damascus he had spoken out boldly in the name of Jesus. (Acts 9:26-27)
Nor did I go up to Jerusalem to those who were apostles before me; but I went away to Arabia, and returned once more to Damascus. Then three years later I went up to Jerusalem to become acquainted with Cephas, and stayed with him fifteen days. But I did not see any other of the apostles except James, the Lord's brother. (Now in what I am writing to you, I assure you before God that I am not lying.) (Galatians 1:17-20)
I'll admit I actually thought Paul was lying to us until I read that last part where he said he wasn't. Note that the passage in Galatians presupposes Acts since Paul says he returned once more to Damascus, yet this is the first time Damascus is mentioned in Galatians.
According to Acts people were trying to kill Paul:
And he was with them, moving about freely in Jerusalem, speaking out boldly in the name of the Lord. And he was talking and arguing with the Hellenistic Jews; but they were attempting to put him to death. But when the brethren learned of it, they brought him down to Caesarea and sent him away to Tarsus. (Acts 9:28-30)
Paul tells it differently:
Then I went into the regions of Syria and Cilicia. I was still unknown by sight to the churches of Judea which were in Christ; but only, they kept hearing, "He who once persecuted us is now preaching the faith which he once tried to destroy." And they were glorifying God because of me. (Galatians 1:21-24)
Acts claims that Paul went back to Jerusalem to settle a debate, while according to Galatians, it was because of a vision he had:
Some men came down from Judea and began teaching the brethren, "Unless you are circumcised according to the custom of Moses, you cannot be saved." And when Paul and Barnabas had great dissension and debate with them, the brethren determined that Paul and Barnabas and some others of them should go up to Jerusalem to the apostles and elders concerning this issue. (Acts 15:1-2)
Then after an interval of fourteen years I went up again to Jerusalem with Barnabas, taking Titus along also. It was because of a revelation that I went up; and I submitted to them the gospel which I preach among the Gentiles, but I did so in private to those who were of reputation, for fear that I might be running, or had run, in vain. (Galatians 2:1-2)
According to Acts, Peter (also known as Cephas for some reason) was the one who received the revelation that gentiles need not get circumcised or keep kosher:
But Peter raised him up, saying, "Stand up; I too am just a man." As he talked with him, he entered and found many people assembled. And he said to them, "You yourselves know how unlawful it is for a man who is a Jew to associate with a foreigner or to visit him; and yet God has shown me that I should not call any man unholy or unclean. (Acts 10:26-28)
The way Paul tells it, Peter changed his tune as soon as the pro-circumcision gang showed up:
But when Cephas came to Antioch, I opposed him to his face, because he stood condemned. For prior to the coming of certain men from James, he used to eat with the Gentiles; but when they came, he began to withdraw and hold himself aloof, fearing the party of the circumcision. The rest of the Jews joined him in hypocrisy, with the result that even Barnabas was carried away by their hypocrisy. But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, "If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews? (Galatians 2:11-14)
Even Barnabas was carried away by their hypocrisy? Not Barnabas! So who's lying? Galatians or Acts? You be the judge. Personally, I'm putting my money on Acts being the liar since we have evidence in Galatians 1:20 that Paul isn't lying.