Well, you don't seem to be getting answers from anybody else, so I'll have a go. I'm afraid that this will be a little brief, but hopefully will give you enough clues as to where to look elsewhere.
There are certain characteristics which are fundamental to composite primary structure, which do not apply to metals.
(1) Anisotropic materials properties (e.g. UTS in the x-axis will be different to UTS in the y-axis). This means that component alignment is incredibly critical, and particular care is needed if, for-example, mixing mod states. Westlands lost a Merlin in flight-test out of Yeovil about 10 years ago or exactly this reason, the accident is fairly well documented and worth looking up.
(2) Atmospheric degredation is a big player; whilst for all reasonable purposes metals behave the same in most climates, composites tend to weaken and gain mass in hot/humid climatic conditions.
(4) Because of mass (moisture) uptake, particularly if operated in hot/humid large aircraft with large composite fractions get heavier, and aircraft CG can shift. This can force you into fairly regular re-weighs rather than purely calculated W&CG. The organisation I work for operates aircraft in temperate climates almost exclusively, and we still feel the need for 5-yearly re-weighs of composite light aircraft, and we do find problems.
(5) BVID (Barely Visible Impact Damage) - is often invisible, weakens a structure, and costs expensive techniques very often to reveal (although it's amazing how reliable the good old coin-tap test is). Tap-test is really only useful however in composite skins / monocoque structures, and little use on (say) composite mainspars and rotors.
(6) Substructure delamination or manufacturing inclusions, ditto.
(7) Fatigue characteristics are totally different to metals, involving microscopic cracking within the matrix, rather than crack propogations as in metals. This requires different training and equipment to spot, and cannot be treated in the same way as metal fatigue.
There are lots of other fascinating problems to do with design and manufacture of composite structures as well, but that should get you going so far as maintenance issues are concerned.
G