Wow, so much information that is not totally correct I just had to jump in. Yes, you can indeed power the Cubie through the 2mm headers, this is exactly what my Baseboard does. You must short or replace D2 with a 0 ohm resistor. You can find the details here
powering-the-cubie-with-the-baseboard
The header under the DC jack has only 2 pins and there are 2 pins on the 2mm header for VCC_5V (U14-43, U15-1). Either the 4-pin header under the DC jack or the 2 pins on the 2mm header will supply the same amount of current. Yes, you may be able to mount a larger pin on the header under the DC jack but that is really splitting hairs as to what can handle more current.
The board has 2 USB ports so maximum power for those ports are 5...@0.5A x 2 so 1A. That leaves you 1A for the A10 processor and associated devices which is more than enough. If you're attaching anything to the GPIO pins that requires extra power those should be powered with an additional power source.
This is the main reason I designed the Baseboard. You bring power in on that board and it then supplies power for the Cubie and plenty of reserve for other devices you might want or need.
Yes, by applying power through the 2mm pins you are bypassing the fuse and protection diodes but if you're experimenting with headers on processor boards you should be skilled enough to always double check before you apply power. With my Baseboard you don't have to worry about bypassing the fuse or diodes because the board is wired to the correct pins.