MySQL 1366 Error on Replication Slave
An answer:

After looking into this further, I determined that the call:

UPDATE mytable SET Flag = 0 where Id = 10

was being called also in a stored procedure which took a parameter of type BIT and did something like so:

UPDATE mytable SET Flag = theFlagValue where Id = theId;

While this worked fine on the master - the mytable would be updated with the correct flag value for any rows matching the Id - it wouldn't work on the slave.

My thought on this is that it involves how the data is serialized when sent to the slave.  That type mismatch was fine on the master but not on the slave.

I was able to modify that stored procedure to take a TINYINT instead and it works flawlessly now.