Would it be Murraya koenigii? (I've not seen red stems on one before.) If so, the thread What's wrong with my Curry Leaf Tree? (Murraya Koenigii) | UBC Botanical Garden Forums may be of interest.
Are the spots like those in these pictures? Apparently, the spots cannot be scraped off. www.flickr.com/photos/destrius/6246361995/ www.flickr.com/photos/destrius/6246360965/ This plant has a leaf spot disease that's caused by the fungus Colletotrichum gloeosporioides but I can't seem to find any pictures of such an infected leaf.
The plant doesn't appear to be too bad off aside from having a few small black spots. I don't know much about this plant but I wonder if it would be better at this time to focus on possibly improving on the tree's cultivation; the leaves appear to be a much lighter green than those seen on other photos online, perhaps due to a nutritional deficiency. A stronger plant would have a better chance in coping with the ailment.