Is there a safety issue with running a AA alkaline cell through 0.3 ohms?
Energy capacity of a AA alkaline cell is about 2000 - 2500 mAh. So it will last maybe half an hour. From your experiment, about 50% of power is dissipated on internal resistance of the cell, internally. This power will be about 1.5- 2W. The alkaline battery cell will become pretty hot, but it won't burst into flames or explode. So you should be safe.