Answer: If the dots are really tiny, they could be spider mites, a common problem on palms. Try spraying a very fine mist onto the newest leaves; if mites are present, the mist will cling to their very fine webs. Spider mites love hot, dry conditions. One control is simply to mist the plant all over, focusing on the new growth and undersides of the leaves, every day. Or an occasional spray with insecticidal soap or a light horticultural oil can help keep the mites under control. Make sure you are watering the plant correctly: rather than applying a little water every day, thoroughly soak the soil, allowing all excess water to drain off, then allow the soil to dry out slightly between waterings. Note, by the way, that an occasional yellow frond is to be expected.
I hope this helps.
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