If my understanding of the time of Paul’s journeys is correct, Paul arrived in Corinth either late summer or near the beginning of autumn in 51 CE. Some scholars place Paul’s appearance before Gallio’s court near the end of his term as proconsul of Achaia, but I think Luke’s “remained many days longer” (NASB) in verse-18 should be seen in light of his “he settled there a year and six months” (NASB) in verse-11. In other words, Paul probably appeared before Gallio nearer to his arrival at Corinth than his departure.
Gallio was born Marcus Annaeus Novatus, the son of the elder Seneca, the distinguished professor of rhetoric (cir. 5 BCE to cir. 40 CE), and brother of the younger Lucius Annaeus Seneca, the Stoic philosopher (cir. 3 BCE to 65 CE) and, at Paul’s time in Corinth, the tutor to the young Nero and future emperor. Gallio came by his name through his father’s friend Lucius Junius Gallio, who adopted Marcus as his heir, whereupon Marcus Annaeus Novatus became Lucius Junius Gallio, using the same name as his adoptive father.
Gallio came to Corinth to take up his appointment as proconsul of Achaia in July of 51 CE. Unlike the magistrates at Philippi or the politarchs at Thessalonica, any judgment Gallio made for or against Paul’s Gospel would have set a precedent to be considered seriously, if not followed, by all governors of any Roman province in the Empire. Paul’s appearance in his court was probably within a very short time of Paul’s breaking off fellowship with the synagogue in Acts 18:6. It makes more sense that the Jewish authorities would have sought to prevent Paul from beginning his ministry in Corinth, seeing as Luke accuses them of blaspheming the Way in verse-6, than trying to end a successful labor. If they were already highly disturbed over Paul’s Gospel, why would they wait several months to accuse him before Gallio?
It seems quite odd to me that Gallio would rule against the Jewish authorities without hearing Paul. Yet, Luke tells us he did exactly that (Acts 18:14-16). Sosthenes, and the Jewish delegates claimed Paul was actively persuading men concerning the worship of God that was contrary to the law (Acts 18:13, 17). The accusation is a broad one, and the term, law, could mean they intended to accuse Paul as one breaking Roman law (cp. Acts 16:21), or it could mean the Jews wanted Gallio to liberalize the current Roman law forbidding government officials from interfering in Jewish religious affairs to also include private interference as well.
It seems Gallio was able to judge their real intent, showing (at least to me) that he was keenly aware of the Messianic movement and its disfavor among Jewish authorities. No doubt, Claudius’ recent expulsion of the Jews over similar circumstances at Rome held sway in his ruling. He was not about to involve himself in such inner religious struggles, and he probably wished to keep the same from happening in Corinth that occurred in Rome. How could any community escape severe economic reversals, if leading men in the community were forcibly removed from the cities commercial industries? Such things need to be avoided, if possible, by any responsible governor.
 See F.F. Bruce, The Book of the Acts, page 373, and Paul, Apostle of the Heart Set Free, page 253.
 An argument against Paul appearing before Gallio near the end of his service as proconsul would be that Gallio was taken ill sometime in 52 CE and took a cruse [see Moral Epistles, 104:1 (http://en.wikisource.org/wiki/Moral_letters_to_Lucilius/Letter_104). If he had taken a cruise on the sea for his health, this presupposes fair weather and that would indicate spring to summer in 52 CE. The fact that the Jews brought Paul before Gallio in Acts 18:12 at the bema (G968), where public discourses were made, shows Gallio’s court was held outside in Luke’s account, implying good weather, so 51CE is more likely, since Gallio’s cruise in 52 CE would have been in good weather, and we don’t know how long the cruise lasted or if he returned before his term in July would have ended.