I noticed that the guy from the Synod you work with in the Dwemer ruin in the Winterhold College quest says he wanted to use the Dwemer oculus thing to detect "certain things" but he cuts himself off. What items of high magical power are the Synod looking for? And why so sneakily? Is it something to fight the Dominion with? Fragments of Numidium?

The remote control.

Just about anything I reckon. They're mentioned that they're trying to curry favor to the higher ups by procuring rare and powerful items.

It's meant to detect magical items, they want to horde magical items. So they can study them and use them, as well as keep them in storage so people have to beg them to get access.