Interesting, to say the least.
Some questions for you: your objective is to measure battery capacity (Ah). And you also want to measure linearity of this capacity. Is this right ?
Internal resistance is a real issue, 1500 mAmp will definitely bring voltage down, below 1 Volt.
Surely. This is due to how batteries work internally, chemically speaking.
- Add some decoupling capacitor (should I ???)
No need. What for ?
- Take into account Base/Emitter current in calculation
It's too small compared to C-E current. But yes, perform a slight adjust.
- Use a MCP3208 12 bits A/D Converter for further accuracy
Time is more important here than instantaneous current. IMHO. So make sure your timebase is accurate. But you're measuring voltage between ground and D2? if so, you're actually (if you compensate for the resistor temperature) measuring current. If you place R2 between ground and battery (-), then you can more accurately see discharge current.
- reconnect to PC for graphical trends of voltage versus time
I might help here 
Send me an email or so if you're interested to test my new serial protocol http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1257971980/23#23
Álvaro