During testing I noticed a significant difference between measured and expected current values. "Well hidden" in the datasheet (page 3 Electrical characteristics) is this line:
Vin- is the culprit here: Basically the part has a pull-down resistor connected to its negative measuring input pin! Really? This 'feature' draws 3.125uA typical per volt of bus voltage, which messes up low current measurements. And this is only a typical value. Every part has to be tested to find its real value.
This is one of the reasons, I decided to change the low current shunt resistor from 500 Ohm to 5 Ohm and bury my dream of measuring nA with this device.
On a side note: The widely popular INA219 has the exact same issue.