Any known issues upgrading from MySQL 5.1.73 to 5.6.21?
ISSUE #1 : Upgrade Path

Your grant tables can get screwed up because you are leaping two versions instead of one.

I just helped someone a week ago because they did just that (MySQL service stops after trying to grant privileges to a user). The solution for that question was to manually fix the mysql.user. Rather than going through that heavy-handed route, there are two ways go about this.

TECHNIQUE #1 : Upgrade the Politically Correct Way


Upgrade From MySQL 5.1 to MySQL 5.5
Run mysql_upgrade --upgrade-system-tables using MySQL 5.5's binaries
Upgrade From MySQL 5.5 to MySQL 5.6
Run mysql_upgrade --upgrade-system-tables using MySQL 5.6's binaries
Generate the System Tables that use InnoDB (See my post InnoDB: Error: Table &quot;mysql&quot;.&quot;innodb_table_stats&quot; not found after upgrade to mysql 5.6) since the MySQL 5.6 version of mysql_upgrade does not create them.


TECHNIQUE #2 : Upgrade Directly from MySQL 5.1 to MySQL 5.6

I already described how to upgrade two versions


Apr 11, 2013 : MySQL upgrade 5.0.88 to latest (Best Reference)
Feb 08, 2012 : will replication from 5.5.20 to 5.0.XX server work?
Jul 26, 2011 : Restoring an old backup to latest MySQL release


ISSUE #2 : FULLTEXT Indexes

If you use FULLTEXT indexes before MySQL 5.6, those tables use the MyISAM Storage Engine. You need to convert those tables to InnoDB (See my post When to switch from MyISAM to InnoDB? under NEED #2). Then, separately tune the InnoDB FULLTEXT options (See my post MySQL FullText search on string shorter than 3 chars returns no rows).

ISSUE #3 : Security Issues

I am sure you are aware of this since you are going straight to MySQL 5.6.21

For the rest who do not know, as of October 16, 2014, Oracle just announced that there are security issues with MySQL 5.5 and MySQL 5.6. This was also announced at Amazon. Both MySQL 5.5.40 and MySQL 5.6.21 will have the security patches in places, so it is best to upgrade to one of these.