Another Point of View

One thing that's very helpfull from playing different toons is having another point of view on things for a change. I believe this not only let you understand other people's role in a party/raid but actuall improves interaction and thus makes an event easier.
For example: when i started tanking i realized how tricky tanking multible mobs was when people open up dps straight away. The other way around it worked aswell, i realised how to better position mobs so dps could stand behind it without pulling a next pack either... stuff like that.

Another example is being melee dps on the Prince in Karazhan, something i experienced for the first time this week on my enhancement shaman.
I've been ranged dps on him and tanked him but i never had to bother with running away each time he was going to enfeeble people (1 health!) and then do his shadownova. All of the sudden i had to keep track of an eye on threatmeters more (110% instead of 130%) aswell as keep the right totems up and watch the boss announcements. If i started running too late i wouldn't make it out savely, even with my runspeed enchant on the boots.
I actually did die once by this, at the feet of the healers as i started moving a second to late... the second time a meteor landed behind which i didn't see and finished me off pretty fast. Better positioning on my part is required next time. (at the side is just as good as behind it, if i make sure i'm not too far up front let him parry my attacks, which is a step closer to the save-spot)

But just not for raids it will help you, if you are more of a pvp person there is knowledge to gain aswell. When i encounter a hunter in combat i know what his weaknesses are and how to avoid his strengths.. or at least i can try to. Same goes for other classes i've played in the past, how to adapt depends on what class you are playing yourself ofcourse.
On my enhancement shaman i try to stay close to the hunters, if they sick their pet on me and i can't get close to the hunter at that point i try to move out of sight and kill the nasty pet first and then heal up. Most of the time this lures the Hunter around the corner aswell where i'm able to reach him more easily... when i would be on my Hunter i'd pull my pet back and keep my distance and try to not get lured too close.
Ofcourse you will be surprised alot with what tricks people can think of using their spells/skills/gear/items and some encounters will teach you more about your own class aswell.
Maybe alts aint that bad afterall...