This week I came across an old known issue reported in May 2010: Master/Slave Replication with binlog_format = ROW and tables without a Primary Key is a bad idea! Especially if these tables are huge.
Why this is a bad idea is described in the bug report #53375:
if one runs DML on a table that has no indexes, a full table scan is done. with RBR, the slave might need to scan the full table for each row changed.
The consequence of this behaviour is that the Slave starts lagging. It was further mentioned: …