MySQL5.6以降で標準準拠のGET DIAGNOSTICSが実装され、その中でMySQLのエラーコードを取得することが可能になります。
MySQL5.7(5.7.2)以降でSTACKEDが追加されています。エラーの詳細を記録するのに使えるかと思います。詳細については次のマニュアルをご参照ください。

GET DIAGNOSTICS Syntax
http://dev.mysql.com/doc/refman/5.6/en/get-diagnostics.html
http://dev.mysql.com/doc/refman/5.7/en/get-diagnostics.html
Worklog: http://dev.mysql.com/worklog/task/?id=2111

MySQL5.6
GET [CURRENT] DIAGNOSTICS

MySQL5.7
GET [CURRENT | STACKED] DIAGNOSTICS

SQL statements produce diagnostic information that populates the diagnostics area. Standard SQL has a diagnostics area stack, containing a diagnostics area for each nested execution context. Standard SQL also supports GET STACKED DIAGNOSTICS syntax for referring to the second diagnostics area during condition handler execution. MySQL supports the STACKED keyword as of MySQL 5.7. Before that, MySQL does not support STACKED; there is a single diagnostics area containing information from the most recent statement that wrote to it.
標準SQLは条件ハンドラの実行中に、第2の診断領域を参照するためのSTACKED診断構文をGETサポートしています。

■ GET CURRENTの挙動
The GET DIAGNOSTICS statement is typically used in a handler within a stored program.
It is a MySQL extension that GET [CURRENT] DIAGNOSTICS is permitted outside handler context to check the execution of any SQL statement.


root@localhost [CONFIRM]> DROP TABLE IF EXISTS t334;
Query OK, 0 rows affected, 1 warning (0.00 sec)

root@localhost [CONFIRM]> GET DIAGNOSTICS CONDITION 1 @p1 = RETURNED_SQLSTATE, @p2 = MYSQL_ERRNO, @p3 = MESSAGE_TEXT;
Query OK, 0 rows affected (0.00 sec)

root@localhost [CONFIRM]> SELECT @p1, @p2, @p3;
+-------+------+------------------------------+
| @p1   | @p2  | @p3                          |
+-------+------+------------------------------+
| 42S02 | 1051 | Unknown table 'CONFIRM.t334' |
+-------+------+------------------------------+
1 row in set (0.00 sec)

root@localhost [CONFIRM]> 

■ GET STACKEDの挙動
The GET DIAGNOSTICS statement is typically used in a handler within a stored program.
It is a MySQL extension that GET [CURRENT] DIAGNOSTICS is permitted outside handler context to check the execution of any SQL statement.
プロシジャー外部での利用の為、エラーになっています。

root@localhost [CONFIRM]> DROP TABLE IF EXISTS t334;
Query OK, 0 rows affected, 1 warning (0.01 sec)

root@localhost [CONFIRM]> GET STACKED DIAGNOSTICS CONDITION 1 @p1 = RETURNED_SQLSTATE, @p2 = MYSQL_ERRNO, @p3 = MESSAGE_TEXT;
ERROR 3004 (0Z002): GET STACKED DIAGNOSTICS when handler not active
root@localhost [CONFIRM]> 

■ CURRENTとSTACKEDの挙動

root@localhost [USER01]> delimiter //
root@localhost [USER01]> CREATE PROCEDURE p ()
    -> BEGIN
    ->   DECLARE CONTINUE HANDLER FOR SQLEXCEPTION BEGIN
    ->     SIGNAL SQLSTATE '01000';
    ->     GET CURRENT DIAGNOSTICS CONDITION 1 @current = RETURNED_SQLSTATE;
    ->     GET STACKED DIAGNOSTICS CONDITION 1 @stacked = RETURNED_SQLSTATE;
    ->     END;
    ->   SIGNAL SQLSTATE '03000';
    ->   END//
Query OK, 0 rows affected (0.00 sec)

root@localhost [USER01]> CALL p()//
Query OK, 0 rows affected, 1 warning (0.00 sec)

root@localhost [USER01]> SELECT @current, @stacked//
+----------+----------+
| @current | @stacked |
+----------+----------+
| 01000    | 03000    |
+----------+----------+
1 row in set (0.00 sec)

root@localhost [USER01]> 

■応用:エラーが発生した原因をテーブルに格納して後で確認

root@localhost [CONFIRM]> CREATE TABLE ids(id INT NOT NULL, UNIQUE(id));
Query OK, 0 rows affected (0.03 sec)

root@localhost [CONFIRM]> CREATE TABLE errors(id INT NOT NULL,RS VARCHAR(16),ME varchar(16),MT VARCHAR(1000));
Query OK, 0 rows affected (0.03 sec)

root@localhost [CONFIRM]> delimiter //
root@localhost [CONFIRM]> CREATE PROCEDURE insert_id(id INT)
    -> BEGIN
    -> DECLARE CONTINUE HANDLER FOR SQLEXCEPTION
    -> BEGIN
    -> GET STACKED DIAGNOSTICS CONDITION 1 @p1 = RETURNED_SQLSTATE, @p2 = MYSQL_ERRNO, @p3 = MESSAGE_TEXT;
    -> INSERT INTO errors VALUES(id, @p1,@p2,@p3);
    -> IF @errno = 1213 THEN
    -> RESIGNAL;
    -> END IF;
    -> END;
    -> INSERT INTO ids VALUES(id);
    -> END;
    -> //
Query OK, 0 rows affected (0.01 sec)

root@localhost [CONFIRM]> delimiter ;
root@localhost [CONFIRM]> CALL insert_id(0);CALL insert_id(1);CALL insert_id(2);CALL insert_id(2);
Query OK, 1 row affected (0.00 sec)

Query OK, 1 row affected (0.00 sec)

Query OK, 1 row affected (0.01 sec)

Query OK, 1 row affected (0.01 sec)

root@localhost [CONFIRM]> select * from ids;
+----+
| id |
+----+
|  0 |
|  1 |
|  2 |
+----+
3 rows in set (0.00 sec)

root@localhost [CONFIRM]> select * from errors;
+----+-------+------+----------------------------------+
| id | RS    | ME   | MT                               |
+----+-------+------+----------------------------------+
|  2 | 23000 | 1062 | Duplicate entry '2' for key 'id' |
+----+-------+------+----------------------------------+
1 row in set (0.00 sec)

root@localhost [CONFIRM]> 

参考)
http://dev.mysql.com/doc/refman/5.6/ja/get-diagnostics.html
http://dev.mysql.com/doc/refman/5.6/ja/diagnostics-area.html
http://dev.mysql.com/doc/refman/5.7/en/get-diagnostics.html
http://dev.mysql.com/doc/refman/5.7/en/diagnostics-area.html