Problems with replication

[David Ford]

Hello everyone,
Sorry to start my posting with a problem but I'm stuck now. I have 2 servers that are identical from a hardware and software perspective. Both servers have Solaris 10 and MySQL 5.6.19 on them. MySQL hosts 4 databases, 2 that don't change much (one or two records a year) and one that is in constant use.
One server is set up as a master, the other as a slave. I had replication running for a couple of days successfully and then it fell over with a duplicate entry error. I tried a couple of things and was not able to make it go away so I locked and backed up the master database, reset the master and then reset the slave, restored onto it, then set the master configuration (CHANGE MASTER TO.....).
When I start slave it starts to process the bin log, but only gets so far before stopping with a 'Duplicate Entry...' error.
No other user has access to the slave, so I know it's not someone else inserting while I'm running the restore or playing back the bin log. I can't ignore the error because the slave must be the same as the master.
I've had a hunt around and the closest thing I can come up with is a bug that was in 5.1 and is still in the manual for 5.6 but that bug is marked as closed. Plus, I've tried setting the logging level from BOTH to STATEMENT just in case.
I'm out of ideas on why the replication is failing.
Anyone able to point me in a new direction?
Many thanks,
David