FYI vinegar is a very effective grass/weed killer. Hopefully the rain will dilute it before it gets a chance to act!
I don't have any good tips. I'd be super annoyed if someone's dog kept pooping on my lawn though.
I remember back in the day, people would fill soft drink bottles with water and place them on the lawn in an attempt to stop dogs pooping on their grass. Not sure if it worked but it sure did look unsightly!