When you talk about such an app it's a good idea to have some basic numbers in mind like .5 second average time to respond to an incoming message and 5seconds worst case. (Picked from thin air but I tend to stick with 1x average 3-10x worst case.)
Now as you scale to 50 or so servers they will start to fail with some regularity and you can't reboot and or rebuild in five seconds so we need to have redundant systems ready. Splitting a shard probably takes longer than five seconds so you need to be proactive about such things. So we need an active rebalancing between shard so they can quickly pass around their load and fast failover incase things fail. These are DB problems but they are only problems because they system need to keep responding quickly as parts of the DB fail.
But this is still DB centric how do you load balance incoming and outgoing requests? (Routing each existing user to the same system every time and letting each system lock data when they want to change their password etc.) How do we recover from data corruption? How do we notice an outgoing or incoming mail server is down? You also have n^2 number of connections between systems as you grow can we keep that many sockets open? (More of an issue is we are segregating the network.) Etc.
PS: These are not hard problems by themselves but they are linked. And there are a lot more where they came from.