Problems with This Schematic?

I need to power 30 servos, so I plan on get one of those large power adapters that can give me 4a, but I can't find any that's around 6v. So theoretically I think I can use a 12v power supply if I wire every two servos in series, and then wire all those pairs in parallel, but are there any practical problems with that schematic that I'm not aware of? Thanks.

Yes, the control signal for the "upper" servo will need to be at a low of 6V and a high of 12V since you've moved its Ground point up.
Nobody says you're limited to 1 supply for all the current.
Use a couple!
http://www.dipmicro.com/store/DCA-0610
Just make sure all supplies are connected to the same ground along with the arduino Gnd.

I do not think it is safe to connect servos in series. The reason is that the servo electronics most likely cannot tolerate voltages higher than about 7 V, and the current consumed by the servo (and the voltage drop) depends very strongly on whether the motor is running. So, you cannot expect each servo to "consume" one half of the power supply voltage.

My advice is to keep the servos independent and use as many 6V power supplies as necessary, budgeting about 1 ampere for each servo that is active at any one time. Connect all the grounds together

I agree with the previous post by jremington.
The current by a servo motor can be 10mA to 1A. The most current is used when the servo starts turning. If you have 30 servos starting to turn at the same moment, you would need a 30A power supply.
If 5V is enough, you could use a switching power supply of 5V.

Thanks to everyone's posts. I expect I'll want to turn individual servos quickly in succession (probably no more than 5 or 10 degrees of rotation each), and I'll do some experimenting to figure out the optimal amount of current I'll need from my power source.

Completely impossible to run the servos in series, they are not resistors and they are
most definitely not a constant load. You'll likely fry them and your Arduino if you try it.

You need a 4.8 to 7.2V supply for most Servos, that's how it is. 5V high current supplies
shouldn't be too hard to find I'd have thought.