There are many good arguments against quickly convening a Third Vatican Council--a notion beloved of Catholics who occupy the portside cabins on the Barque of Peter.
The most obvious is that Catholicism has barely begun to digest the teaching of Vatican II on the nature of the Church, the universal call to holiness, and the reform of the episcopate, the priesthood, consecrated life, and the lay vocation in the world. Until the dramatic change in Catholic self-understanding that Vatican II mandated is fully internalized and implemented--until the Church understands itself as a mission, not as an institution that has a mission (as one among many things it does)--there seems little sense in convening Vatican III.
One might also argue that another ecumenical council would be a distraction from the evangelical mission to which Vatican II called the Church, and especially the Church's bishops. As it is, bishops spend far too much of their time in meetings. Would the preaching of the Gospel, which, according to Vatican II, is the first responsibility of bishops, be advanced by gathering the entire world episcopate into a global mega-meeting for three or four months of the year, over a period of years?
Then there's the question of resources. Any Vatican III would cost vast sums of money: would such an expenditure be the best use of the Church's resources? (As Father John O'Malley reports in "What Happened at Vatican II?," one of the reasons Pope Paul VI was determined to conclude Vatican II in December 1965 was that the Council was simply costing too much.)
These are all good reasons why a general council would be a bad idea for the foreseeable future. But there's another issue here, one that raises an intriguing question about any future council, no matter when it's convened: Where could Vatican III (or Lateran VI, or Trent II, or Lyons III, or whatever-the-future-council-is called) possibly be held?
Vatican I (1869-70) met in one transept of St. Peter's, because there were only 737 bishops attending. Some 2,800 bishops participated in the four sessions of Vatican II, which met in the fall months of 1962, 1963, 1964 and 1965, although at any one session there were between 2,000 and 2,500 bishops present--and they filled the entire, vast nave of St. Peter's, seated on bleachers built high above the basilica's marble floor. Add the ecumenical observers, the Council periti (advisers), and other functionaries with access to the Council aula (as the reconfigured basilica was called), and St. Peter's was packed full.