Powering Multiple Servos From One Battery- What is my circuit missing?
One thing to ask, it is not clear if you are going to run the Arduino Uno off the same battery, or off a different battery?

If the same battery, then you are likely going to need to create an V+ output for the Uno, but will need to ensure that any drain from multiple servo's running are not going to impact on the voltage supplied to the arduino, and also that the voltage supplied is compatiable with the Uno (e.g. don't run 6V+ into the 3V outlet)

Just to note as well, the Arduino Uno has (to my knowledge) only has about 6 PWM pins which is what you will need to drive the servo's through the signal pin. You can add I2C PWM expanders which give you more pins (e.g. https://www.adafruit.com/product/815) but YMMV