Battery percentage inaccurate
Let me simplify since I see we have debaters.

You should calibrate your battery:

After you use your battery, as low as it will go, below 20%. Plug it into A/C Power until it is definitely fully charged. Wait an extra 20 minutes to make sure that it is fully charged. Then you need to: 

1) Remove the battery stats file:
rm /data/system/batterystats.bin

This will prevent you from seeing any discrepancies in the usage of your battery &amp; the battery stats.

2) Wipe the dalvik cache: 
rm /data/dalvik-cache/* 

You stated that an app is showing your voltage levels as being correct, so you may need the app's cache cleared.

3) Then Reboot:
reboot

This is what causes the kernel to re-calibrate your battery, when the phone is rebooted after a full charge.