Wall water marks on wall with damage to the plastering.
If there is one thing I look out for when buying an apartment would be Water Leakage. Sorting out a water leakage issue could be costly.
Some times you got to be suspicious when you see a patch with a fresh coat of paint. When I see things like that I normally touch the surface of the wall to feel if it's damp.
So far the place our place looks pretty ok.
For some other areas to look out for would be in the toilet tiled area and especially near the windows.
Notice stain marks coming from the grouting area. Normally to solve this problem will require hacking the tiles.
The worst kind is the one in the picture below. Bubbling of the paint work. Even bubbling normally is a result of water swelling between the wall and paint. Uneven bubbling like the one below is a result of moisture and mold. Mold is not good. Can't image this happening in a home with young children.