Answer: The symptoms you describe lead me to believe your magnolia is suffering from two things: a canker disease caused by fungus, that has attacked the branches, and mites, that are coating the undersides of the leaves.
To combat the canker, prune off affected branches, cutting back an inch into symptom-free tissue to remove any marginally affected wood. Dip your pruners or saw into a 10% bleach solution between cuts to prevent spreading the fungal spores with your tool. If at least half of the tree shows symptoms, then I'm afraid it's best to replace the entire tree. Less advanced symptoms of canker include elongated, target-like lesions that are blue-gray, and later develop cracks.
Mites and other pests are usually drawn to plants that are already "out of balance," such as your canker-infected tree. Take a look at a leaf using a magnifying lens, and if the "dust particles" have legs, then the dust is probably mites. These pests prefer dry, dusty conditions, and are especially attracted to water-stressed plants. If spring moisture has been lacking, water the tree deeply about once per week. Don't overwater, though, and make the soil sodden, or you'll invite other problems. To get rid of the mites, first try driving them off with a good spray of water from your hose. This will dislodge many of them and also create a humid environment that doesn't favor them. If they are persistent, try a light horticultural oil spray; follow label directions carefully.
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