From what I could tell while I was working on this quest, there are several "glitches" that may be resolved soon. Sometimes kills wouldn't register as rescues, even when no one else was around. It looked like if I killed a zombie outside of the area marked on the map, I wouldn't get credit. Also, if multiple people were killing the same zombie, only the one with the "killing blow" would receive quest credit. This includes pets! It took me a while to figure out why, even with no one else attacking the zombie, and being in the marked region, I wasn't getting credit. On a hunch I switched my pet to passive when the zombie got low, and lo! Credit was awarded!
So, to summarize:
- only kill zombies in the marked region of the map
- turn pets to passive if you've got 'em
- killing blow gets the credit, not the person who marked the zombie in the first place
- feel free to snipe kills from others, but be aware it'll probably happen to you too!