Spider mites
Fine speckling and webbing can point to tiny mites.

What to look for
Inspect the undersides of leaves for tiny moving dots, pale stippling and sometimes fine webbing. A magnifier or gently tapping a leaf over white paper may make them easier to see.
What to do
Separate the plant and rinse suitable leaves, including undersides, with water. Check nearby plants and repeat inspection. If the problem persists, choose a product labeled for mites and the plant, following its directions.