Agree about the damage looking like spider mites. I've never done anything about spider mites but thorough showering and for very established infestation, spritzing with rubbing alcohol. The trick is noticing the problem in time. Removing the most affected leaves is the best first step, then the thorough rinsing/showering. If you want to do both, spritz the alcohol, then rinse & shower after.
Is the air in your home very dry? That can be an invitation for SM. Does the pot have a drain hole? If it's not just an illusion from the top-down angle of the pic, it looks very small compared to the size of the tree.
