The first thing you look at when checking walls is looking at how is it constructed, if it's a new home they are probably made with sheetrock or drywall, and if it's an older house, they might have plaster.
Next, the most obvious feature of a wall is the wall covering, but is it in good condition? If its paint, is it chipping, or faded? Wallpaper can look nice but is often very specific to the taste of the last homeowner, and usually, the new homeowner would want to replace it with a different wall covering. If this is your desire, removing wallpaper can be easy, if it was installed correctly.
It is also essential to look at the texture of the wall, to see if it is bulging in any areas, or unusual in any way to the rest of the walls. These differences could indicate work that has been done due to remodeling or repair work because of water damage.
Checking the walls of a house that you are looking to buy is an essential part of the buying process.