MySQL relay log corrupted, how do I fix it? Tried but failed

A MySQL v5.1.61 relay got corrupted when the machine suddenly shut down. I tried to fix it but it didn't work.
— How do I fix it? Did I do something wrong?

As far as I've read, corrupted MySQL relay logs are easily fixed:

change master to master_log_file='<Relay_Master_Log_File>',
                 master_log_pos=<Exec_Master_Log_Pos>;

where Relay_Master_Log_File and Exec_Master_Log_Pos are listed by:
mysql> show slave status;

However when I did change master status ..., I got a primary key violation error. How is that possible? Is the above procedure no correct, or is e.g. some +1 missing?

_{(For now I've simply re-imported a --master-data mysqldump from the master to the slave, and this solved the problem. However, in the future, doing that might not be appropriate.)}

Here follows details about my particular problem:

mysql> show slave status \G
*************************** 1. row ***************************
               Slave_IO_State: Waiting for master to send event
                  Master_Host: the-master-host
                  Master_User: replication
                  Master_Port: 3306
                Connect_Retry: 60
              Master_Log_File: mysql-bin.000021
          Read_Master_Log_Pos: 33639968
               Relay_Log_File: mysql-relay-bin.000271
                Relay_Log_Pos: 2031587
        Relay_Master_Log_File: mysql-bin.000020
             Slave_IO_Running: Yes
            Slave_SQL_Running: No
              Replicate_Do_DB: the_database
          Replicate_Ignore_DB: 
           Replicate_Do_Table: 
       Replicate_Ignore_Table: 
      Replicate_Wild_Do_Table: 
  Replicate_Wild_Ignore_Table: 
                   Last_Errno: 1594
                   Last_Error: Relay log read failure: Could not parse relay log event entry. The possible reasons are: the master's binary log is corrupted (you can check this by running 'mysqlbinlog' on the binary log), the slave's relay log is corrupted (you can check this by running 'mysqlbinlog' on the relay log), a network problem, or a bug in the master's or slave's MySQL code. If you want to check the master's binary log or slave's relay log, you will be able to know their names by issuing 'SHOW SLAVE STATUS' on this slave.
                 Skip_Counter: 0
          Exec_Master_Log_Pos: 66395191
              Relay_Log_Space: 36559177
              Until_Condition: None
               Until_Log_File: 
                Until_Log_Pos: 0
           Master_SSL_Allowed: No
           Master_SSL_CA_File: 
           Master_SSL_CA_Path: 
              Master_SSL_Cert: 
            Master_SSL_Cipher: 
               Master_SSL_Key: 
        Seconds_Behind_Master: NULL
Master_SSL_Verify_Server_Cert: No
                Last_IO_Errno: 0
                Last_IO_Error: 
               Last_SQL_Errno: 1594
               Last_SQL_Error: Relay log read failure: Could not parse relay log event entry. The possible reasons are: the master's binary log is corrupted (you can check this by running 'mysqlbinlog' on the binary log), the slave's relay log is corrupted (you can check this by running 'mysqlbinlog' on the relay log), a network problem, or a bug in the master's or slave's MySQL code. If you want to check the master's binary log or slave's relay log, you will be able to know their names by issuing 'SHOW SLAVE STATUS' on this slave.

And this is what I did:

mysql> stop slave;
mysql> reset slave;
mysql> change master to master_host='the-master-host', master_user='replication', master_password='the-password', master_log_file='mysql-bin.000020', master_log_pos=66395191;
mysql> start slave;

And this is what happened, a PK error:

131122 15:17:29 [Note] Slave I/O thread: connected to master 'replication@the-master-host:3306',replication started in log 'mysql-bin.000020' at position 66395191
131122 15:17:29 [ERROR] Slave SQL: Error 'Duplicate entry '71373' for key 'PRIMARY'' on query. Default database: 'the_database'. Query: 'insert into ...  values ...', Error_code: 1062
131122 15:17:29 [Warning] Slave: Data truncated for column 'date' at row 1 Error_code: 1265
131122 15:17:29 [Warning] Slave: Duplicate entry '71373' for key 'PRIMARY' Error_code: 1062

I think I followed the recommended procedure (see links just below), still there was a PK error :-( ? http://bugs.mysql.com/bug.php?id=26489, search for "Workarounds". http://mhbarr.wordpress.com/2013/07/26/mysql-slave-corrupted-relay-log/ http://stackoverflow.com/a/14438408