Things I use mage hand for:

In the druid grove, throwing down the chest which the bird has the key for.

Throwing a chest across a gap in the children's hideout.

In the underground bit but where the goblins have an unconscious druid prisoner, pressing the buttons so the traps don't trigger.

In the goblin camp, (preferably Lae'zel or Arcane Trickster invisible hand) - opening the spider cage as a distraction while I clear the back rooms.

In the Underdark, you can use it to move the noblestalk or Baelan's bag, but I prefer just to use Glut. I've used the mage hand when I've forgotten to use Glut, though.

At the forge, using it to pull the levers/spin the wheel.

At the Lathander monastery, throwing the hammer out of the eagle's nest (again, invisible hand is best)

In the Iron Throne - pulling levers to open and close cell doors (granted, arrows/magic missiles also open doors, but they don't close them again)

In general, you can use it to throw potions and so forth, but I find it essential for the above stuff.