There are a couple, and they are insidious. From http://geoff.greer.fm/2012/08/12/character-encoding-bugs-are...:
This is when I discovered that InnoDB limits index columns to 767 bytes. Why is this suddenly an issue? Because changing the charset also changes the number of bytes needed to store a given string. With MySQL’s utf8 charset, each character could use up to 3 bytes. With utf8mb4, that goes up to 4 bytes. If you have an index on a 255 character column, that would be 765 bytes with utf8. Just under the limit. Switching to utf8mb4 increases that index column to 1020 bytes (4 * 255).
And later:
You might say, “OK, now we’re finished, right?” Ehh… it’s not so simple. MySQL’s utf8 charset is case-insensitive. The utf8mb4 charset is case-sensitive. The implications are vast. This change in constraints forces you to sanitize the data currently in your database, then make sure you don’t insert anything with the wrong casing. At work, there was much weeping and gnashing of teeth.
Good luck. The real solution is to switch to something that isn't MySQL. The project in that post ended up switching to Cassandra. For new SQL stuff, I now use PostgreSQL.
Edit:
To those of you who point out that utf8mb4_unicode_ci is case-insensitive, we did try that. This whole fiasco happened two years ago, and I don't remember what the show-stopper was, but we decided not to use that collation. Whatever issues we had with it were bad enough to warrant switching to utf8mb4_bin and sanitizing everything. Really, the solution is to switch away from MySQL and forget about collations and encodings.