I would have thought you might have fewer problems unless you have the same pests. A lot of the tropical plants make do with pest damage because there is no off season for bugs, no winter kill. Pests are around year round, but they do still go through cycles. The best defense with fungal diseases like Anthrachnose and powdery mildew is to regularly cleanup the leaves and infested fruit as soon as you see it. Prune the tree to keep it more open to let more air and light in and if the tree isn't too tall, you will need to spray the tree before it blossoms or there won't be any fruit. Blossom midge can make blossoms drop and they are hard to control. 90% of mango trees in residential areas have some issues. About half of the blossoms drop just from wind alone. Anthrachnose isn't pretty, but it is found on riper fruit. Luckily I like my mango half ripe anyway.
Happy gardening in Hawaii. Gardens are where people grow.