Whenever I try to combine two types of potions, first I drag them both out of my inventory out onto the ground. Then I drag one "potion" over the other to get a new one. Problem is, it always ends up using all of my potions in said pile, yet only gives me one new potion in return. Is there a way to reduce those potion piles to only one potion? In general, if you have more than one of an object in your inventory, how do you only drop one?

You don't need to drop them. Just open your inventory and move one potion pile over the other and you will get a new potion, with only one being subtracted from each pile.

Open your inventory, hold control, click on the multi-item, drag and drop it on the ground (or anywhere), holding control will cause a dialog which gives you the means to drop the quantity input much like the trade window does.
I drag a pile of [insert item here] over another pile and drop it inside the inventory window. I think most items never max but gold is limited to 50,000 per pile if I remember correctly.
If it doesn't work inside the inventory, open a barrel or chest along with your inventory, drag the item to the barrel window,drop it, drag it back to your inventory and drop it on the pile you want to add it to. This should work as well . . .=)