Implications of/Fix damp on shared wall
Tracking water infiltration can be difficult with the root cause not obvious. Sometimes you luck out and find a spot on the roof, in a valley or around a vent pipe or chimney that is the culprit. Since this is a town house with a shared wall, i wonder if the tenant on the other side has had the same moisture problems? Is there a possibility of damage or trapped moisture inside the wall? 
  If you are looking to purchase, I would advise you to have it looked at and corrected by a professional before closing. If this defect is found during a home inspection, the current owner should be responsible for the repair of the leak and the discolored wall. At minimum, an allowance in the selling price should be made if you accept responsibility for the fix. In your specific case, don't plan on an easy self fix before you purchase the property, what you hope may be a minor repair may turn out to be very expensive.  Also, is the shell of the building covered by a condo Common area clause in the declaration of Condo? If so, the condo assoc will be responsible for the fix.  There are lots of questions here. Be careful and don't underestimate the problem.