lol dual core only leh
btw, previously wikipedia got stated the exynos code
like s3 using exynos 4412, but now just stated it using exynos 4 quad, don't have the number ~.~
if not mistaken exynos 5450 is 28nm quad core right ?

This is one reason. They can't make enough to fulfill demand so they use some other SOC.
Another reason on why they can't keep up is because they are also producing stuff for other companies like Apple.
Samsung Mobile has to bid with other companies to get the production capability from Samsung Semiconductors, if they don't they will be hit with some anti-competitive laws etc. Even though both are owned by Samsung, both subsidiaries can't just go all out and stop producing stuff for other companies, plus they probably make a lot of money making stuff for apple etc. haha.
The exynos 5250 is better because it'll be based on the ARM A15 architecture while the quad in the S3 is still based on the old A9 architecture. There's no devices that has an A15 based processor yet out to the consumer market if I'm not mistaken, once it's out, it'll be a beast. The closest to it would be the snapdragon S4 which is based on the Krait architecture which is basically A9 with a bunch of A15 stuff incorporated into it.

Probably the earliest we'll see a phone with an A15 based processor in it is late this year, maybe the next nexus or something, or note 2 or early next year, unless the new iphone uses A15.

Nope, it's cooked into the S3's ROM by samsung. You'll lose all this features if you flash a custom rom unless the rom has it as well.
Who knows if Samsung will implement it into the note in a future update but for now, no.