So after some investigation it turns out this is due to emoji characters being 4-byte Unicode, which don't work with MySQL - they just get removed when adding to the database. They can be used if the columns use utf8mb4 character set, but unfortunately that's only available on MySQL 5.5+.
So for now I've made a change to Q2A that will remove 4-byte characters in posts to avoid this bug. Will be part of 1.7.3.