What are these dots?
 

Recently aquired a struggling unknown cymbidium. Repotted and its showing signs of new growth. Also noticing these dots on the leaves. What could it be? It is is a bright south window with semi direct sun for most of the day

Looks like damage from boisduval scale to me. Take a look right down at the pseudobulbs and ease out the dry sheaths. If there is what appears to be a white fluffy mess in there you have this scale.

I removed alot of dry old psudo bulbs, leaves and rotten roots when I re-potted and dont see any white fuzz or scale looking stuff on the bulbs(photo) also a better photo of what the dots look like up close...

I think that it may be old damage. Cym leaves seem to attract all sorts of insults, that ultimately don't do any harm. I have seen this sort of thing, subsequent new growth is fine. So I would not worry much.