Mega 2560 powered with 7V don't work correctly I have an Arduino Mega 2560  with a GPRS seeedstudio shield and an USB Host CircuitsAtHome shield which work fine when powered with USB or with an adjustable voltage regulator set at 8V.

When I set this voltage regulator at 7V (minimum voltage from the spec to get the better efficiency) I am still reading 5V and 3.3V on the pins of the Arduino and all the leds of the Arduino and the GPRS shield seems fine but the USB Host CircuitsAtHome shield seems to not work properly.
I cannot debug it using the console because if I plug the USB cable, everything works fine...

Why 7V fail while 8V is ok?

The adjustable voltage regulator can provide up to 5A which is plenty.
The Voltage-Regulator has a dropout-voltage of 1,2V, but in line to the regulator is a diode, which adds another minimum 0,7V (dont know the exact part number, so i guessed the voltage of a Si-diode at ~1A). So you have to supply at least 5 + 1,2 + 0,7 = 6,9V. I presume the circuit doesnt draw a constant current all the time, so from time to time the regulator cant supply the 5V because you sink under the necessary dropout-voltage of the rehulator/diode-combination.

-> Use 8V  or bypass the Diode D1 (with a solder-bridge) and use 7V if its a must and you are sure the input-polarity is always correct.   

Arduino-Mega-2560-schematic: http://arduino.cc/en/uploads/Main/arduino-mega2560_R3-sch.pdf