There's no real way around it - there are very few quests where the quest item is a common item, such as Jungle Remedy in STV. For that one I collect the amount and then trade it to one of my toons until they all have it.

For the other quest items (that you can't trade) you have to switch between your characters and loot them. My setup is my main on my laptop and the rest on my desktop. They are right next to each other, so the most that I have to do is swivel my chair. I tab between the windows on my desktop to switch charaters to loot quest items. I run the desktop WoWs in fullscreen, renamed with HotKeyNet, and some very basic macros on the alts. Tabbing between the toons, while not instant, doesn't take very much time. My desktop isn't the greatest and I was getting performance issues running in windowed mode. I use the MaxFPSBk macro to drop the framrate of the minimized WoWs and don't really have any issues not being able to see every one of the characters in their own window. I also don't PVP so your milage may vary.

I try to stay away from collection quests as much as possible - some are unavoidable, especially if you want to continue a quest chain. When I do have to do a spawned collection, once one of the alts is looting the spawn I tab to the next toon so that I am ready and have my cursor over the spawn site ready to go.