The main threat to the health of dracaena comes from the scale insects and thrips. If you observe a premature shedding of the leaves, this might also signal a spider mite infection. Deal with those by washing off as many insects as possible and then applying a gentle insecticide.
Often, brown spots form on the leaf blades, which leads to drying of the leaves and the overall loss of vitality. Dry air and insufficient watering might be responsible for such plant behavior.
Excessive bright lighting poses a risk of burning the foliage, which also appears as dark spots, so it's best to shade the flowerpots from the scorching sunlight.