How can I keep my neighbours dog from messing all over my grass?

Get a print out of the leash law and that they are suppose to clean up after their dog and hand it to them or put it on their front door or whatever. Maybe even include a super duper p**per scooper with the note.

Not knowing your state here is some general links

Overview of State Leash Laws

The next to last resort may be scooping it into their yard.