Is it the designers' intent that a non-spellcaster be able to fire magic missiles with that wand? Or should this be treated as errata?
This absolutely looks like designers' intent.
The Wands have a variety of restrictions on attunement and they seem to be connected to the rarity / power of the wand.
- Uncommon: Magic Detection, Magic Missiles, Secrets, Web^
- Rare: Binding^^, Enemy Detection^, Fear^, Fireballs^^, Lightning Bolts^^, Paralysis^^, Wonder^^
- Very Rare: Polymorph^^
^ attunement
^^ attunement by spellcaster
More powerful spell wands have a more restrictive attunement requirement. This seems intentional. If you look at the various magical Staves many of them have even more specific requirements than the wands. Like the Staff of Healing requiring attunement by a Bard, Cleric or Druid.
From the rules on creating your own magic item, here is the excerpt on Attunement (DMG 285).
Use these rules of thumb to help you decide:
- If having all the character in a party pass an item around to gain its lasting benefits would be disruptive, the item should require attunement.
- If the item grants a bonus that other items also grant, it's a good idea to require attunement so that characters don't try to collect too many of those items.
That last point is really important here.
Do I care if the Rogue has 5 Wands of Detect Magic? Probably not. It's not a really powerful spell. Do I care if the Wizard is walking around with 5 Wands of Fireball? Absolutely! What about the Barbaian? Even more so!
The restrictions not only seem intentional, they seem rational and balanced. Especially given how many classes get access to some magic at some point. I think everyone but the Barbarian has some magic using archetype.
Yes
Many parts of the text on attunement specify that they only apply to items that require attunement. Surprisingly, actually attuning isn't one of those parts. The DMG ( p. 138) states:
Attuning to an item requires a creature to spend a short rest focused
on only that item while being in physical contact with it (this can't
be the same short rest used to learn the item's properties)..., at the
end of the short rest, the creature gains an intuitive understanding
of how to activate any magical properties of the item, including any
necessary command words.
None of this demands that the item in question requires attunement.
Also note that you must spend a different short rest (ie, another hour) to identify what the properties of this magic item are (attunement does not reveal that). And yet another hour to drop attunement to this item, since you can only be attuned to up to three magic items at a time. Still, you will be able to learn the number of charges an item has without the Identify spell.
NOTE: Spending a short rest to Identify the item (DMG p. 136) will not reveal how many charges the item has left, by rules as written (RAW). Your DM may permit it to do so, but RAW states that the Identify spell reveals charges remaining (both stated on DMG p. 141, and PHB p. 252, in the text of the spell), while the description of mundanely identifying the item (with a short rest) (DMG p. 136) does not.
Best Answer
Yes, it can use the wand
The creature animated by tiny servant is a creature and the spell places no restrictions on what kind of actions it can take, or be commanded to take.
Therefore, it is able to use any general magic items, including a wand of magic missiles.
For other magic items, a tiny servant can even attune to (up to three) magic items, but not ones that have requirements (such as being a spellcaster) that it does not fulfil (such as the wand of fireballs). It is also limited by its carrying capacity — which for a Tiny creature with a Strength of 4 is 30 lb — but this is not a problem for most items.