There are three GND pins on the Arduino UNO pinout. As I'm trying to design a mixed signal PCB to act as an Arduino Shield, I wonder how I should connect those pins, i.e. to the analog or digital ground plane? Or can I assume the left pin row is digital (thus on digital ground) and the right analog (next to the analog inputs, on analog ground)?
Those three grounds are all tied together on the Arduino. If you want to have separate grounds for analog and digital, don't tie them both to the Arduino. Maybe tie the digital ground to the Arduino ground and AC couple the output from your analog circuit so it has it's own independent ground.