There are a number of indicator that your building has a damp issue. Dark patches appearing on walls is one very clear sign, another is the peeling or lifting of wallpaper. If you notice a damp musty smell in the air this may also be an indicator that you have damp, as well as any rotting wood (skirting boards, door frames, etc.).
The more obvious signs are walls being wet to the touch or visible water droplets appearing on the surface of the wall. Mould or mildew growth is another more serious indication of damp because mould can cause health issues to the inhabitants.