If I were to set up cyclical replication between a MySQL 5.6 master server and a MySQL 5.1 master server, what are some things that could potentially go wrong?
Also, the 5.6 MySQL does not have GTID enabled.
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Replication from MySQL 5.x to 5.6 has a bear trap just waiting for you.
In Michael's comment, he stated the politically accept premise : "MySQL supports replication from one major version to the next higher major version.". He also said "this setup isn't guaranteed to work in either direction."
I have a very interesting caveat on going from 5.x to 5.6: There are some rare occasions when a binlog event from a pre-5.6 master cannot be interpreted by 5.6 slave and stops replication cold. I wrote about this in January (See my post mysql replication master 5.5 slave 5.1 error on create database)
I concluded my old post with this
If this crazy scenario was possible from a MySQL 5.5.30 Master to MySQL 5.6.21 Slave, (as I have shown happen and two maintenance cycles to correct), then the reverse is far more likely (the reverse being a new Master and an older Slave).
You do not want circular replication for 5.1/5.6. While you can replicate from 5.1 to 5.6, please don't stay long in that setup. The binlog format differences are very slight, but different enough to break replication. As @RickJames said "Simply, don't do it. Get the 5.1 upgraded ASAP."
While I could expound just on circular replication, I refer you to