The pulldown would ensure it doesn't start on while the outputs are high impedance, once they are set as outputs and either high or low it doesn't matter, you could probably get away without them but thereon almost always there
how much draw on the 5v line are you using? Dropping ffrom 12v to 5v is basically wasting more than half the power as heat with a linear regulator
the 5v line draw is minimal - if i remove the status LED's (or put them on the emitter side of the transistors) - the draw would be the Arduino, DS1307 & MCP23008 + the current draw on the transistor gates = i am guessing it is not using very much power but its not sipping power either... also there are a ton of pulldown/pullup resistors on the pins. The draw on the opamp is < 10ma. I was going to limit the LED draw to 140ma.
I have pretty much -0- experience with power supplies - i have always used a 9 or 12 v wallwart with LM7805 .... having said that, my prototype circuit is using the L4931 regulator in a TO-92 (!) package - it is running a bit hot. I was planning on switching out the L4931 in the RBBB i am using for the prototype with a LM7805 but have not gotten around to doing it (desoldering is my least favorite activity)
If you have any power supply recommendations to improve the circuit, i would appreciate!