For rainy day patrol, carry a towel. The city gives you a raincoat to repel water but not all of it. You'll need to dry off, get up spilled coffee or wipe your sweaty brow—any old hand towel will do. Also, pre-moisturized wipes are good for getting ugly stuff off your hands.
Carry a a pocket knife and multi-tool. They require maintenance; a dull knife and rusty pliers are useless.
One little plastic tackle box can store oodles of needful things, such as paper clips, safety pins, chalk, extra pen/pencil, lip balm, few bandages, antiseptic, uniform device clasps (damn-its), extra flashlight bulbs and over the counter helpers (allergy, aspirin and antacids) and other things that make life better. The box keeps it tight, dry and not scattered.
Watch the weather forecast. Even though most local forecasters can't fall out of tree and predict that they will hit the ground, watch them anyway. If they say tonight is cool, take your jacket and gloves; this is the night you are on the interstate directing traffic in subzero weather. If they even hint of precipitation, take your rain gear and towel.
Pay attention to special events in your precinct. You can't rely fully on the department to tell you everything. The night you have the entertainment district is the night it is 'all you can drink night' at a biker bar. Pick up the local entertainment papers and pay attention to fliers—you noticed the veterans took that night off, didn't you?