Biotic and abiotic causes of tree health problems really do go hand in hand. Once a tree has been afflicted to a moss or fungus or the like it becomes even more prone to pest infestation. Most trees that are suffering from health problems have a primary and secondary cause for their illness, so they must be treated for both to truly recover. The primary reason for health problems in most trees just deals a first blow, but it can be the secondary source that really does the tree in. This is why all health issues have to be addressed, not just one, or the other.
All trees may react differently when they are ill, but some things to watch out for are falling leaves before the appropriate season, late or lack of blossoming, branches that do not have any leaves on them, holes in the trunk or branches, evidence of insect activity, or dry leaves that have an odd texture to them are all signs of an ill tree. The best thing you can do at this point is to call a professional. While you may be able to make an educated guess as to what is wrong, only a professional can tell you for sure and then either treat the tree, or let you know how to treat the tree yourself if at all possible.
Trees are like people, they need time, attention, love, and care. Even with the best care, a tree may become ill and suffer from some problems, but the better care that is taken the less likely your tree is to have health problems.