International surrogacy allows prospective parents from countries where surrogacy is not regulated or prohibited to create a family. So, a major advantage of international surrogacy is that it brings these families the chance to have a family, who would otherwise be unable to.
As for the disadvantages, probably the number of legal issues related to this practice are the main complication derived from this option. One should be well informed about the law in each country before making the final decision, including the law in their home country. Otherwise, you may experience serious trouble, with the child being rendered "stateless" in the worst-case scenario.