-Syu and -Syyu are exactly the same thing if all the package servers you use are up to date with each other or you only use one mirror.

Managing the mirror list is a pain, so I don't do it. I just installed pacman-mirrorlist instead, and let that take care of it (I can't remember if I needed any other packages to automate things).

But that means it changes mirrors pretty regularly, as various mirrors are dropped because they didn't update as fast as other mirrors.

Using -Syyu instead of -Syu means pacman disregards the update time advertised by the server and checks the version of every package it tracks (or something like that), instead of just checking those that could have been updated since the last time it checked. This tends to help keep things in check if you change mirrors frequently.

I don't think there are any downsides on the client side, but it probably puts more load on the servers.

EDIT: If you have a newer version of a package from one mirror, and then update with an older mirror, -Syu will ignore it unless it's needed by other packages. -Syyu will ask you to downgrade the package (with -Suu or -Syyuu or whatev) to make sure you stay in sync. I think. This all gets really complicated and beyond my understanding of pacman (especially if a package removes a prerequisite in a later version), and mirrors are generally pretty well kept in sync.