I am the OP. I have been very happy where I live. The landlord has always fixed this in a timely manner. I am not moving because of this. SO, stop suggesting it.
The problem is above the windows so "putting a pan down" doesn't work on a windowsill. I have small bowels to catch water with the towels.
I have written to landlord and manager with pics of wall and condition as a necessary step before calling health Inspector.