Once the pot has been placed on the stove, the stove becomes immovable until the pot is removed from the unit. This is done by inspecting the contents of the stove and dragging the pot off the stove top (at which point it will either move to empty inventory slots or drop to the ground [still containing its juicy loot goodies]).
Items placed inside pots will remain there even if you clear space in your inventory. You need to manually remove items from the pots.
Items in pots inside the inventory don't register on the quick select num line. This means if you put your compass in the pot, you can no longer use it to navigate.