I'm a big fan of "pinning" mechanisms where any time a user performs a write to your database you set a cookie that lasts for a few seconds and causes any subsequent requests from that user to go to the lesser, not a replica.
This solves the stale-read-after-write problem and ensures users will see any changes that they have personally made.
This does assume a mostly-reads, occasional-write application (which defines most of the applications I've worked on in my career).
So given that kind of application, what are the problems I'm not considering that I should look out for with a read-replica on a different continent?