I have read somewhere that Mr.magic eraser would safely work on the headliner. It kinda make sense in a way because, you don't want to wet the old headliner as it will just drop down with old glues it have.
I have some marks in my car as well that look like they would be hard to get off and a friend of mine seen it and mentioned using baby wipes. He said it'll come right off. I still haven't tried it but I will eventually.
personaly i use a steam cleaner that i rent from home depo .. cost like 25$ you get it for 4 hour ! so you just rent it at 6pm and you got its till tomorow .. or just tint the got damn thing black .. lol