I had the same issue with my mango. And it turn out to be that I was overfeeding it.

I found this online.

Leaf Burn

Problems in the soil extend to problems with your mango tree leaves, such as dry brown spots. Such problems include too much nitrogen or excessive salts in the soil. Both problems come as a result of over-fertilization. Fertilizers increase the amount of salt in the soil and raise the nitrogen levels. Excessive amounts of these elements cause leaf burn in your mango tree, and leaves develop dry, brown spots of patches. If the leaf burn is severe, the leave may die and drop from the tree.

Read more: http://www.ehow.com/info_12311248_mango-trees-dry-brown-spots-leaves.html#ixzz2xkMu8c2k

Thanks, but I can rule that out... haven't been fertilizing.