convert utf8_general_ci Tables to utf8mb4_general_ci - What to expect?

[Andreas Schnederle-Wagner]

Hey there,
we got a pretty large legacy DB which we need to convert from utf8_general_ci to utf8mb4_general_ci for Full UTF8 Support.
All Data should be valid UTF-8 (mysqli_set_charset('utf8') on App side)

Am I right with my expectations that there shouldn't be any Problems doing this?
Or are there caveats I'm overlooking?

And what's the best way for such a conversion? (Already Googled Hours & Hours ... but there are so many different advises out there which makes it pretty hard to find out the "right way" ... :-/)
Thought about using: ALTER TABLE `{$table}` CONVERT TO CHARACTER SET utf8mb4 COLLATE utf8mb4_general_ci;

Thank you, bye from rainy Austria
Andreas Schnederle-Wagner

ps) A little bit Off-Topic in this MySQL Board I guess - but anyone knows if switching from mysqli_set_charset('utf8') to mysqli_set_charset('utf8mb4') can have any Side-Effects? (with existing and not yet converted utf8 Tables)