One of the characters is an Arcane Trickster who has Mage Hand. She's been pretty creative in using the spell, and I wanted to know what restrictions the spell had.
The PCs were in a castle and were getting shot at through arrow slits by Drow. She made an incredibly high Perception check, so she could see the crossbow. She used the mage hand to pull the bolt from the crossbow. I thought this was amusing and allowed it, although I wasn't sure if this was RAW.
The PCs were behind a locked door that potentially could be opened from the other side. She wanted to use the mage hand to open the door from the other side. I ruled that she couldn't see the other side, so she couldn't use the spell in that way.
So, do you need to be able to see the mage hand to use it? It can be used to pick pockets, but how much can it be used to harass monsters / NPCs?
Mage hand description (PHB page 256):
A spectral, floating hand appears at a point you choose within range. The hand lasts for the duration or until you dismiss it as an action. The hand vanishes if it is ever more than 30 feet away from you or if you cast this spell again. You can use your action to control the hand. You can use the hand to manipulate an object, open an unlocked door or container, stow or retrieve an item from an open container, or pour the contents out of a vial. You can move the hand up to 30 feet each time you use it. The hand can’t attack, activate magic items, or carry more than 10 pounds.
Possibly related question: Can any spellcaster use Mage Hand to perform a Sleight of Hand check?