By exploiting idle time on volunteer machines, desktop grids provide a way to execute large sets of tasks with negligible maintenance and low cost. Although desktop grids are attractive for their scalability and low cost, relying on external resources may compromise the correctness of application execution due to the well-known unreliability of nodes. In this paper, we consider a very challenging threat model: correlated errors caused either by organized groups of cheaters that may collude to produce incorrect results, or by buggy or so-called "unofficial" clients. By using a previously described on-line algorithm for detecting collusion and characterizing the participant behaviors, we propose a scheduling and result certification algorithm that tackles collusion. Using several real-life traces, we show that our approach minimizes both replication overhead and the number of incorrectly certified results.