Here's another example of basement walls that are staining from moisture that is accumulating on the other side of the basement wall and working its way through the wall.

I don't recommend painting these walls, it might look nice but you're actually trapping the moisture in the concrete block wall and over time this could cause it to to deteriorate.

If the concrete wall was to start deteriorating, there's very little you can do and eventually the walls will have to be replaced.

I don't recommend building another wall over this, because mold and mildew and even fungus can start to accumulate in between the new wall you build and the existing concrete foundation wall.

If you look at the upper left hand corner of the picture, you will see some mold or moss growing on the basement wall.

Simply clean the moss or mold with some bleach or chlorine and if these aren't working that good, you can always use muratic acid. All of these products work great for cleaning concrete block walls.

Make sure that you read the directions and only use these products in well ventilated areas.

Home Repair Tip - Simply keep the area clean and I wouldn't recommend painting over it or building a wall to cover it up. Keep the basement well ventilated and watch these areas for mold and mildew, and the biggest problem over time, could be the deterioration of the concrete block wall. Try to keep the wall as dry as possible and this can be done by fans or heaters.