If you can, pick up refuse that you find which someone else has left behind. Do not cut new switchbacks or shortcut existing switchbacks. Back in the city, the pet may be lovable and well-behaved, and allowed to roam, unfettered. But in the backcountry, things are much different. A dog's bark in the backcountry is out of place, startling and even frightening both man and wild animals.
Dogs poop everywhere and anywhere.
Masters typically don't clean it up. Dogs fight each other and they don't care where. In the middle of a narrow trail, my dog was on a short leash, at my side, the other dog was running loose and attacked my dog. On another occasion, the owner just laughed. Always keep dogs leashed, on trail, and tied up, in camp.