I don't think you should have previous tenant come back to fix. He moved out without fixing himself now it's your responsibility to make it ready for next tenant.
Also, when you inform the previous tenant, make the list as short as possible in case he want to make a big deal out of it. Make sure items on the list is iron-clad his responsibility.
1. garbage was not collected. You disconnect the service before the last collect?
Let the next tenant put it on the curb, no big deal.
2. back yard screen door is broken.
Replace and deduct, clearly it's damaged.
3. dog poop at back yard all places.
Have someone clean, bill and deduct. Pet damage to lawn.
4. Oven was dirty, professional house cleaning was unable to clean it.
Replace a new oven and deduct. Unable to clean means damaged. If you are nice you ask for only 1/2.
5. two closet door stopper in bed room are missing.
Just add new ones, 5 min $10, no need to fuss over it.
6. lots of scratches on master bedroom and living room windows frame.
Have handyman repaint, deduct. Scratches are most likely caused by dogs looking out window and saw squirrels.
Next time when you rent to pet owner, collect pet deposit for things like #3 and 6.