Question on having a MySQL 5.1 replicate from a MySQL 5.6 DB I have a question in regards of what potential issues that might happen with a MySQL 5.1 DB that replicates from a MySQL 5.6 DB.  

I know the risks involved based on resources such as http://dev.mysql.com/doc/refman/5.6/en/replication-compatibility.html  and also https://serverfault.com/questions/262936/is-replication-from-mysql-5-5-master-to-a-5-1-slave-possible 

However, this is a very special case because I am trying to replace the MySQL 5.1 DB with a 5.6 version, and the only way to have minimum downtime is to have a 5.6 DB set up first and then let it replicate from the 5.1 DB, which will in turn also replicate from the 5.6 DB to form a cyclic replication. The purpose of this is to ensure that during the switchover (when the 5.6 DB will be the active one receiving the live writes instead of the 5.1 ), no write data would be lost. 

I was curious if anyone has ever had this kind of setup before with the 5.1 DB replicating from the 5.6 DB, and if there were any issues you encountered. I am not sure what SQL commands in the 5.6 DB could be problematic for the 5.1 DB during replication. 

To be exact, the 5.6 version is 5.6.21 and the 5.1 version is 5.1.73

Thanks
Believe it or not, I once wrote a post about why you should not do that (How can I disable utf8mb4 entirely on MySQL 5.5?). However, in the spirit of my old post and the commentary in it from @ChristopherSchultz, I will go out on a limb and tell you how you can do it, then tell you why you should not.
I once wrote a post about the home position of any empty binary log:

120 in MySQL 5.6
107 in MySQL 5.5
106 in MySQL 5.1
 98 in MySQL 4.1/5.0
MySQL master binlog corruption

Over the years in this forum, I learned from someone (I think it was either Aaron Brown or Morgan Tocker) that there is a universal position for all binary logs regardless of the MySQL Version: position 4.
I once put that in an answer (Mar 05, 2013 : MySQL Replication without stopping master). In Step 06 from my answer I wrote this:
CHANGE MASTER TO
MASTER_HOST='10.1.20.30',
MASTER_PORT=3306,
MASTER_USER='repluser',
MASTER_PASSWORD='replpass',
MASTER_LOG_FILE='mysql-bin.000001',
MASTER_LOG_POS=4;

I also used position 4 in these other posts

Apr 02, 2014 : How do I fix Replication event checksum verification failed while reading from network. Error_code: 1743
Mar 05, 2014 : Risk of changing clocktime on MySQL server host

Rarely do I repeat this info in any other posts for a reason. Personally, I fear that binlog events might be represented differently from version to version in terms of the size (in bytes) of each event. Believe it or not, over the past two weeks I have been upgrading DB Servers from MySQL 5.5. to MySQL 5.6. Due to mixed mode binary logging, there have been rare events when replication breaks and you cannot reset it from binlog files and positions by standard replication techniques. I have had to hose binary logs on Master, copy data, and setup replication from scratch a few times (5 out 400 VMs, but it still happened 5 times). I am very sure that replicating from a new Master to an old Slave would cause many more problems along these lines.
Therefore, I can only say that you can do it theoretically and MySQL may not object, that is, until MySQL Replication encounters a binlog event that is in a format it does not recognize and cannot interpret.
GIVE IT A TRY AT YOUR OWN RISK !!!
UPDATE 2014-11-18 22:32 EST
Just for official reference, this example CHANGE MASTER TO command
CHANGE MASTER TO
  MASTER_HOST='master2.mycompany.com',
  MASTER_USER='replication',
  MASTER_PASSWORD='bigs3cret',
  MASTER_PORT=3306,
  MASTER_LOG_FILE='master2-bin.001',
  MASTER_LOG_POS=4,
  MASTER_CONNECT_RETRY=10;

appears in the MySQL 5.6 Documentation. It's also in the MySQL 4.1 Documentation.
Thus, position 4 has always been known (I have only known a couple of years). Notwithstanding, I trust MySQL Replication from old Master to new Slave (but not on a permanent basis). I do not trust MySQL Replication from new Master to old Slave.
UPDATE 2014-11-19 17:47 EST
Please don't go down the Circular Replication path as it just adds to the risk of lost binlog events due to different versions. You should always replicate one direction to a newer version. Then, just failover to the newer version.