Try "Lime Off" from Jungle products.
I tried the vinegar approach on a tank and cover that has been sitting for about ten years. Other than it stinking up the place, I did not have much success at all.
Using the "Lime Off" is doing a really good job of removing the water\mineral marks. It is taking me several coatings, but it all appears to be coming off slowly. I also tried it on another tank that has not been sitting all that long and it did a great job of clearing it up. It is safe for glass and acrylic. Cleans up nice
Some LFS may carry it, but I had to order mine on line. Here is the link.
http://www.bigalsonline.com/StoreCatalo ... =0&offset=
Hope it helps!