I don't know if class actions exist on a world scale, but some international bodies have pronounced on the problem of the absence of an appeal, notably the Organization of American States in its review of Canadian asylum procedures. It has commented on the fact that the absence of a review is a problem, and the UN High Commission for Refugees has as well.
In terms of individuals who feel they have not been properly treated, there are a couple of recourses. There's recourse, for example, to the Committee Against Torture, on an international scale, and there have been some successful applications. Some of them have criticized features, including the lack of an appeal in the Canadian asylum system. The problem is that none of these are specifically binding in terms of forcing Canada to enact legislation or to respect legislation that's on the books.