What are some known hazards with cyclical replication between two MySQL master servers? 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.

Thanks IS
Cringe, gag, etc.

5.1 and 5.6 differ by 2 major versions.  Replication is 'guaranteed' to work one direction, not the other.

Don't turn on GTIDs in 5.6; 5.1 will not like it.

Don't use any features new to 5.5 or 5.6.

Simply, don't do it.  Get the 5.1 upgraded ASAP.