It already past two months after 5.6.13 is released.
There are many bug fix on InnoDB and Replication.
If you use MySQL5.6.xx, please check if your MySQL can be fixed trouble with this version.

http://dev.mysql.com/doc/relnotes/mysql/5.6/en/news-5-6-13.html

Previously, program options could be specified in full or as any unambiguous prefix.
For example, the –compress option could be given to mysqldump as –compr,
but not as –comp because the latter is ambiguous. Option prefixes now are deprecated.
Option prefixes are no longer supported in MySQL 5.7; only full options are accepted.
(Bug #16996656)

The C API libmysqlclient shared-library .so files now have version 18.1.0
(up from version 18.0.0 used in MySQL 5.5). 18.1.0 can be used as a replacement
for 18.0.0. (Bug #16809055)

In batch mode, mysql formatted result status messages such as “”Query OK, 1 row affected”” but did not print them. Now these messages are not formatted.
(Bug #69486, Bug #16971432)

Performance; Important Change; InnoDB: InnoDB would fail to open a tablespace that has multiple data files.

Performance; InnoDB: A code regression introduced in MySQL 5.6 negatively impacted
DROP TABLE and ALTER TABLE performance. This could cause a performance drop between
MySQL Server 5.5.x and 5.6.x. (Bug #16864741, Bug #69316)

Performance; InnoDB: When innodb_thread_concurrency is set to a non-zero value,
there was a possibility that all innodb_concurrency_tickets would be released after
each row was read, resulting in a concurrency check after each read.
This could impact performance of all queries.
One symptom could be higher system CPU usage. We strongly recommend that you
upgrade to MySQL Server 5.6.13 if you use this setting.
This could cause a performance drop between MySQL Server 5.5.x and 5.6.x. (Bug #68869, Bug #16622478)

InnoDB: The server would crash during a memcached set operation.
The failure was due to a padded length value for a utf8 char column.
During a memcached update operation, a field from an old tuple would be copied with
a data length that was less than the padded utf8 char column value.
This fix ensures that old tuples are not copied. Instead, a new tuple is created each time. (Bug #16875543)

InnoDB: When CHECK TABLE found a secondary index that contained the wrong
number of entries, it would report an error but not mark the index as corrupt.
CHECK TABLE now marks the index as corrupt when this error is encountered,
but only the index is marked as corrupt, not the table. As a result, only the
index becomes unusable until it is dropped and rebuilt. The table is unaffected. (Bug #16914007)

InnoDB: InnoDB would attempt to gather statistics on partially created indexes.
(Bug #16907783)

InnoDB: A full-text search using the IN BOOLEAN MODE modifier would result in
an assertion failure. (Bug #16927092)

InnoDB: A memory leak would occur when inserting or replacing a row in a full-text
search index on a table with more than 96 columns. (Bug #16809167)

InnoDB: Stale InnoDB memcached connections would result in a memory leak.
(Bug #16707516, Bug #68530)

InnoDB: Creating a table with a comment or default textual value containing an
apostrophe that is escaped with a backslash would sometimes cause the
InnoDB storage engine to omit foreign key definitions. (Bug #61656, Bug #12762377)

and so on ………….

1) Download and Preparation.

[root@HOME002 src]# rm mysql-5.6.11-linux-glibc2.5-i686.tar.gz
rm: remove 通常ファイル `mysql-5.6.11-linux-glibc2.5-i686.tar.gz'? y
[root@HOME002 src]# wget http://dev.mysql.com/get/Downloads/MySQL-5.6/mysql-5.6.13-linux-glibc2.5-i686.tar.gz/from/http://cdn.mysql.com/
--07:22:25--  http://dev.mysql.com/get/Downloads/MySQL-5.6/mysql-5.6.13-linux-glibc2.5-i686.tar.gz/from/http://cdn.mysql.com/
dev.mysql.com をDNSに問いあわせています... 137.254.60.11
dev.mysql.com|137.254.60.11|:80 に接続しています... 接続しました。
HTTP による接続要求を送信しました、応答を待っています... 302 Found
場所: http://cdn.mysql.com/Downloads/MySQL-5.6/mysql-5.6.13-linux-glibc2.5-i686.tar.gz [続く]
--07:22:26--  http://cdn.mysql.com/Downloads/MySQL-5.6/mysql-5.6.13-linux-glibc2.5-i686.tar.gz
cdn.mysql.com をDNSに問いあわせています... 125.56.218.10, 125.56.218.62
cdn.mysql.com|125.56.218.10|:80 に接続しています... 接続しました。
HTTP による接続要求を送信しました、応答を待っています... 200 OK
長さ: 299105519 (285M) [application/x-tar-gz]
Saving to: `mysql-5.6.13-linux-glibc2.5-i686.tar.gz'

100%[=====================================================================================================>] 299,105,519  541K/s   in 8m 8s

07:30:34 (599 KB/s) - `mysql-5.6.13-linux-glibc2.5-i686.tar.gz' を保存しました [299105519/299105519]

[root@HOME002 src]#

[root@HOME002 src]# tar zxvf mysql-5.6.13-linux-glibc2.5-i686.tar.gz
mysql-5.6.13-linux-glibc2.5-i686/bin/innochecksum
mysql-5.6.13-linux-glibc2.5-i686/bin/myisam_ftdump
mysql-5.6.13-linux-glibc2.5-i686/bin/mysql_waitpid
mysql-5.6.13-linux-glibc2.5-i686/bin/mysqld_safe
mysql-5.6.13-linux-glibc2.5-i686/bin/perror
mysql-5.6.13-linux-glibc2.5-i686/bin/resolveip
mysql-5.6.13-linux-glibc2.5-i686/bin/msql2mysql
mysql-5.6.13-linux-glibc2.5-i686/bin/mysqlbinlog
mysql-5.6.13-linux-glibc2.5-i686/bin/mysqltest
mysql-5.6.13-linux-glibc2.5-i686/bin/mysqlbug
mysql-5.6.13-linux-glibc2.5-i686/bin/mysql_plugin
mysql-5.6.13-linux-glibc2.5-i686/bin/mysql_setpermission
mysql-5.6.13-linux-glibc2.5-i686/bin/myisamchk

[root@HOME002 src]# mv mysql-5.6.13-linux-glibc2.5-i686 /usr/local/
[root@HOME002 src]# cd ..
[root@HOME002 local]# pwd
/usr/local
[root@HOME002 local]# ls -lh
合計 124K
drwxr-xr-x  2 root  root  4.0K  1月  8  2013 bin
drwxr-xr-x  2 root  root  4.0K  3月 30  2007 etc
drwxr-xr-x  2 root  root  4.0K  3月 30  2007 games
drwxr-xr-x  2 root  root  4.0K  1月  7  2013 include
drwxr-xr-x  3 root  root  4.0K  1月  7  2013 lib
drwxr-xr-x  2 root  root  4.0K  3月 30  2007 libexec
drwxr-xr-x  3 root  root  4.0K  1月  7  2013 man
lrwxrwxrwx  1 root  root    33  6月 22 10:18 mysql -> mysql-5.6.12-linux-glibc2.5-i686/
drwxrwxr-x 13 mysql mysql 4.0K  1月 25  2013 mysql-5.5.29-linux2.6-i686
drwxrwxr-x 13 mysql mysql 4.0K  2月 16  2013 mysql-5.6.10-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4.0K  4月 28 16:11 mysql-5.6.11-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4.0K  6月 22 10:09 mysql-5.6.12-linux-glibc2.5-i686
drwxr-xr-x 13 root  root  4.0K  9月 14 07:48 mysql-5.6.13-linux-glibc2.5-i686
drwxr-xr-x  2 root  root  4.0K  3月 30  2007 sbin
drwxr-xr-x  5 root  root  4.0K  1月  7  2013 share
drwxr-xr-x  2 root  root  4.0K  9月 14 07:49 src
[root@HOME002 local]#

[root@HOME002 local]# /etc/init.d/mysql stop
Shutting down MySQL...                                     [  OK  ]
[root@HOME002 local]#

[root@HOME002 local]# rm mysql
rm: remove シンボリックリンク `mysql'? y
[root@HOME002 local]#


2) MySQL Preparation and Start MySQL. (Binary and data is moved to latest version of MySQL.


[root@HOME002 mysql-5.6.12-linux-glibc2.5-i686]# cp -rp data/*  /usr/local/mysql-5.6.13-linux-glibc2.5-i686/data/
cp: `/usr/local/mysql-5.6.13-linux-glibc2.5-i686/data/test/db.opt' を上書きしてもよろしいですか(yes/no)? y
[root@HOME002 mysql-5.6.12-linux-glibc2.5-i686]#

[root@HOME002 local]# chown -R mysql:mysql mysql-5.6.13-linux-glibc2.5-i686/
[root@HOME002 local]# chmod -R 755 mysql-5.6.13-linux-glibc2.5-i686/
[root@HOME002 local]# ln -s mysql-5.6.13-linux-glibc2.5-i686/ mysql
[root@HOME002 local]#


[root@HOME002 local]# ls -l
合計 124
drwxr-xr-x  2 root  root  4096  1月  8  2013 bin
drwxr-xr-x  2 root  root  4096  3月 30  2007 etc
drwxr-xr-x  2 root  root  4096  3月 30  2007 games
drwxr-xr-x  2 root  root  4096  1月  7  2013 include
drwxr-xr-x  3 root  root  4096  1月  7  2013 lib
drwxr-xr-x  2 root  root  4096  3月 30  2007 libexec
drwxr-xr-x  3 root  root  4096  1月  7  2013 man
lrwxrwxrwx  1 root  root    33  9月 14 07:57 mysql -> mysql-5.6.13-linux-glibc2.5-i686/
drwxrwxr-x 13 mysql mysql 4096  1月 25  2013 mysql-5.5.29-linux2.6-i686
drwxrwxr-x 13 mysql mysql 4096  2月 16  2013 mysql-5.6.10-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  4月 28 16:11 mysql-5.6.11-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  6月 22 10:09 mysql-5.6.12-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  9月 14 07:48 mysql-5.6.13-linux-glibc2.5-i686
drwxr-xr-x  2 root  root  4096  3月 30  2007 sbin
drwxr-xr-x  5 root  root  4096  1月  7  2013 share
drwxr-xr-x  2 root  root  4096  9月 14 07:49 src
[root@HOME002 local]#
[root@HOME002 local]# ls -l
合計 124
drwxr-xr-x  2 root  root  4096  1月  8  2013 bin
drwxr-xr-x  2 root  root  4096  3月 30  2007 etc
drwxr-xr-x  2 root  root  4096  3月 30  2007 games
drwxr-xr-x  2 root  root  4096  1月  7  2013 include
drwxr-xr-x  3 root  root  4096  1月  7  2013 lib
drwxr-xr-x  2 root  root  4096  3月 30  2007 libexec
drwxr-xr-x  3 root  root  4096  1月  7  2013 man
lrwxrwxrwx  1 root  root    33  9月 14 07:57 mysql -> mysql-5.6.13-linux-glibc2.5-i686/
drwxrwxr-x 13 mysql mysql 4096  1月 25  2013 mysql-5.5.29-linux2.6-i686
drwxrwxr-x 13 mysql mysql 4096  2月 16  2013 mysql-5.6.10-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  4月 28 16:11 mysql-5.6.11-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  6月 22 10:09 mysql-5.6.12-linux-glibc2.5-i686
drwxr-xr-x 13 mysql mysql 4096  9月 14 07:48 mysql-5.6.13-linux-glibc2.5-i686
drwxr-xr-x  2 root  root  4096  3月 30  2007 sbin
drwxr-xr-x  5 root  root  4096  1月  7  2013 share
drwxr-xr-x  2 root  root  4096  9月 14 07:49 src
[root@HOME002 local]#


[root@HOME002 local]# /etc/init.d/mysql start
Starting MySQL..........                                   [  OK  ]
[root@HOME002 local]#

3) Check Version & Data.


mysql> select @@version;
+------------+
| @@version  |
+------------+
| 5.6.13-log |
+------------+
1 row in set (0.00 sec)

mysql>


mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
| DB_REPLICATION     |
| mysql              |
| performance_schema |
| test               |
+--------------------+
5 rows in set (0.20 sec)

mysql> select database();
+------------+
| database() |
+------------+
| test       |
+------------+
1 row in set (0.00 sec)

mysql>

mysql> show tables;
+----------------+
| Tables_in_test |
+----------------+
| TABLE001       |
| timestamp_chk  |
| timestamp_chk2 |
+----------------+
3 rows in set (0.11 sec)


------------- Insert Data at Master Database.
mysql> insert into TABLE001(title,comment) values('after-uprate11','Master MYSQL is upgraded to 5.6.13.');
Query OK, 1 row affected (0.40 sec)

mysql>

------------- Confirm at Slave Database.
mysql> select * from TABLE001 order by id desc limit 0,1;
+----+----------------+-------------------------------------+
| id | title          | comment                             |
+----+----------------+-------------------------------------+
| 23 | after-uprate11 | Master MYSQL is upgraded to 5.6.13. |
+----+----------------+-------------------------------------+
1 row in set (0.00 sec)

Upgrade finished on slave.
これで、スレーブ側のアップグレード確認が終わったので、マスターをアップグレードして終了。

—————————
MySQL 5.7ももう準備進んでいるのですね。

MySQL 5.7 Release Notes