I was pleased to see that the G12 could be triggered remotely and especially pleased to discover that I already had the remote! I'd bought the RS60-E3 some years ago to use with a film camera (anyone remember those?). Anyway, it still works and works well. The trick (if there is one) is to treat the RS60-E3 the same as you would the on-camera shutter button: press the button on the RS60-E3 lightly (just as you should do for the on-camera shutter button), think "Focus", hesitate (or watch the G12 screen for the green rectangle confirmation) and then finish off pressing the button.
If you only fully press the RS60-E3 button then the result is the same as if you had fully pressed the G12 on-camera shutter button: the G12 tries to focus but gives up and fires after a brief internal even if focus has not been fully achieved. The result is images that seem randomly focused or unfocused.