At the time you had the7805 regulator attached, was there anything else attached to the Arduino - USB cable, power supply, etc?
Can you tell if the old sketch is still running when you apply power to the Arduino's DC jack?
I presume you have now removed all external components from the Arduino.  When you plug it into the computer, does the power LED come on?  Can you try another USB port on the same computer, or another computer?

The error you're seeing is roughly 0.3%.  That's not far from the 0.2% error I measured on an Uno a little while ago:
http://arduino.cc/forum/index.php/topic,69316.msg516645.html#msg516645

If your custom board is using a crystal then it's likely to be much more accurate.  My Freetronics "Eleven" (an Uno clone with a crystal in place of the Uno's resonator) is accurate to roughly 40ppm.

If you can tolerate a small amount of drift, then I'd recommend building a second copy of your custom board, or buying something like the Freetronics Eleven.  If you need better precision and can put the microcontrollers close together on the same board then it's possible to run off a single crystal (beware, the second clock is not wired in the same way as the first).

Hours in one year: 525,946

Ouch!

I could get a 16MHz 5V Arduino down to approx 1uA.

If you could get the avr to run on a 16Mhz crystal with less than 1ua, you should contact Atmel,

Getting an avr to run below 50ua is easy, even on a crystal. Getting it to run below 10ua on a crystal is difficult. Getting it to run below 1ua on a crystal is out of this world.

We're talking about the power saving modes, in which the CPU is stopped.  What are you talking about?

I took a quick look at some datasheets for a few 3V lithium coin cells.  The ones I looked at quoted self-discharge rates around 0.1uA.

Duracell claim a self-discharge rate equivalent to 10uA in their Alkaline AA cells.

[Current drawn by an Atmega328p with external 16 MHz Crystal = 13 mA]

Current drawn by an Atmega328p with external 16 MHz Crystal = 13 mA

That sounds reasonable if you are not using any power-saving techniques.  Using code similar to Nick's demo linked above, I could get a 16MHz 5V Arduino down to approx 1uA.  My multimeter is not good enough to read these very low currents with any accuracy, so I cannot say if the real current was less than that.  The datasheet claims 0.1uA at 3V, and I've no reason to doubt that.

Using Nick's code below I was able to get down to 400uA with everything unlugged which suggests the rest is down to the board peripherals?

That much could easily be drawn by the voltage regulators, even if you are injecting power downstream from the regulators' output.  In addition the RTC spec shows that it draws 100-200uA.  The simplest solution for ultra-low power would be a standalone '328 chip.  Myself I like to use Sparkfun's Pro-Micro because you don't need a chip socket or PCB, but it requires some minor surgery to cut the trace from the voltage regulator.

Wonder why it was called "Organic Glass", something lost in translation?

It's an unusual term, but plexiglass is an organic molecule (unlike "normal" glass), so I can see where it comes from.

You know Pin-1 is labelled "TXO" on the Pro Mini, right?

[Serial]

There are 2 ways you could do this:
- Skip the bootloader and run the ArduinoISP sketch on the Leonardo
- Use the Leonardo as an USB-to-serial interface and program the 328 via the bootloader as normal

The second option is probably easier, but entails writing a short sketch for the Leonardo to link Serial and Serial1.

I think this is the one you need:
http://proto-pic.co.uk/break-away-headers-right-angle/

Bad serial data will not cause flickering (aside from the regular 3 flashes after a reset).  You've got a bad contact somewhere, possibly on the CP2102 interface.  You tested the RX/TX loopback already, so it may be just the 5V output pin that's dodgy.  Try powering the breadboard from a separate 5V supply (not forgetting to common the grounds).

Oscilloscope on pin 3

I took your sketch, commented out the initial delay, and put it on a 16MHz Arduino Pro (essentially just an ATmega328 with a crystal and power supply).  With the FTDI interface connected or disconnected I couldn't get the sketch to fail -- it ran fine after a power-on reset or an external reset.  So I'm afraid I don't know what was causing the symptoms you describe.

In addition to Ninoscript's comments, Pin 10 on the Duemilanove should be connected to Reset on the ArduPilot, not the other way around.  Are the grounds connected?