Some dates replicated with a +4 offset
So, yes, the problem was the time_zone settings. 

As mentioned in the docs, if time_zone=SYSTEM, MySQL will do a timezone calculation, otherwise, it (presumably) will not. 

When you INSERT/UPDATE the data as a string, MySQL stores it "as is". If you INSERT/UPDATE the data with NOW(), it stores the current UTC value.

Since my slave had time_zone=US/Eastern, it never did the timezone calculation, so some of my dates were off by +4 hours.

This seems to have fixed the problem of dates in other tables as well.

That's my story and I'm sticking to it. :-)