I have murraya koenigii, but it has very few pest problems. The aromatic leaves are repellent to most pests. Even the white flies don't bother it. I did find that is is susceptible to some things like scale, powdery mildew, phytophthora, and phyllostictina murrayae (curry leaf spot). I found a file picture of a curry leaf with the same symptoms. As the disease progresses the spots will become sunken brown and more necrotic. As an added bonus I found out that curry leaf is a favorite host plant of the Asian citrus psyllid which causes Huanglongbing disease on citrus trees. The curry leaf is immune and even if the psyllid feeds on it, it does not contract or pass on the disease. Curry plant is being investigated as a possible host trap plant to try to control the psyllid.
However, I did find out what your problem is a fungal disease.
There was no information about the leaves being edible, but I usually don't eat any leaves infested with fungi. To prevent the spread of spores, I suggest removing the plant and do not replant in the same place. Cool wet conditions favor the disease.
Your plants look close to a fence. Better air circulation and a sunny location might help. It never gets really cool here. 49 degrees has been the lowest I have seen and it was just for a day. My plant has to be pruned a few times a year to keep it from becoming a tree. It is already over my head now and I am in the process of cutting the trunk down to a more manageable height. I have to cut off the flowers so it does not set seed.
https://books.google.com/books?id=4yb-V ... ot&f=false
https://en.wikipedia.org/wiki/Phyllosticta
https://www.ncbi.nlm.nih.gov/pubmed/29648945