So taking from 2024 era monk, but I'm sure it mostly applied to 2014 era;
MARTIAL ARTS
You gain the following benefits when unarmed or wielding only Monk weapons, provided you aren’t wearing armor or wielding a Shield.
• You can make an Unarmed Strike as a Bonus Action.
• You can roll 1d6 in place of the normal damage from your Unarmed Strikes or Monk weapons.
• You can use Dex. instead of Str. for the attack and damage rolls of your Unarmed Strikes and Monk Weapons. In addition, when you use the Grapple or Shove option of your Unarmed Strike, you can use Dex. instead of Str. to determine the save DC.
QUESTION
barring the use of Kensei monk, would a monk holding, say, a dart, or a sling, therefore "wielding" them, lead to the Martial Arts feature being disabled?
The set of weapons that count as "monk weapons" is slightly different between the 2014 and 2024 rules, but in either case wielding a weapon not on the appropriate list disables the Martial Arts feature, just as if you were wearing armor.
In practice, I suspect most DMs probably wouldn't enforce that if you were just holding a dart in your hand for some reason without any intent to use it as a weapon, but that situation is probably extremely rare.
2014: Any simple melee weapon that doesn't have the Heavy or Two-handed property
So the following are valid Monk weapons (2014 PHB): Club, Dagger, Hand Axe, Javelin, Light Hammer, Mace, Quarterstaff, Sickle & Spear
*Underlined are thrown weapons
2024: all simple melee weapons, additionally any martial weapons with the light property
So the following are valid Monk Weapons (2024 PHB): Club, Dagger, Great Club, Hand Axe, Javelin, Light Hammer, Mace, Quarterstaff, Scimitar, Shortsword, Sickle & Spear
*Underlined are thrown weapons
As such there are multiple thrown weapons which are usable with Martial Arts die, Darts are different as they are simply not melee weapons to begin with, they are ranged weapons. For the Thrown weapons that qualify, nothing in Monk does says that Martial Arts die only applies to melee attacks, so throwing a light hammer should still use the Martial Arts die and you can use Dexterity instead of Strength.
In the case of holding a non-valid weapon then yes, you can't use the martial arts die, but really, why would you? About the only time I think you would, it would be for making attacks outside of melee/thrown range.
One thing I do find fun is that under 2024, Monk technically now has proficiency in hand crossbow, probably some weird tactic somebody can think up with that one.
So taking from 2024 era monk, but I'm sure it mostly applied to 2014 era;
MARTIAL ARTS
You gain the following benefits when unarmed or wielding only Monk weapons, provided you aren’t wearing armor or wielding a Shield.
• You can make an Unarmed Strike as a Bonus Action.
• You can roll 1d6 in place of the normal damage from your Unarmed Strikes or Monk weapons.
• You can use Dex. instead of Str. for the attack and damage rolls of your Unarmed Strikes and Monk Weapons. In addition, when you use the Grapple or Shove option of your Unarmed Strike, you can use Dex. instead of Str. to determine the save DC.
QUESTION
barring the use of Kensei monk, would a monk holding, say, a dart, or a sling, therefore "wielding" them, lead to the Martial Arts feature being disabled?
That's correct.
The set of weapons that count as "monk weapons" is slightly different between the 2014 and 2024 rules, but in either case wielding a weapon not on the appropriate list disables the Martial Arts feature, just as if you were wearing armor.
In practice, I suspect most DMs probably wouldn't enforce that if you were just holding a dart in your hand for some reason without any intent to use it as a weapon, but that situation is probably extremely rare.
pronouns: he/she/they
2014: Any simple melee weapon that doesn't have the Heavy or Two-handed property
So the following are valid Monk weapons (2014 PHB): Club, Dagger, Hand Axe, Javelin, Light Hammer, Mace, Quarterstaff, Sickle & Spear
*Underlined are thrown weapons
2024: all simple melee weapons, additionally any martial weapons with the light property
So the following are valid Monk Weapons (2024 PHB): Club, Dagger, Great Club, Hand Axe, Javelin, Light Hammer, Mace, Quarterstaff, Scimitar, Shortsword, Sickle & Spear
*Underlined are thrown weapons
As such there are multiple thrown weapons which are usable with Martial Arts die, Darts are different as they are simply not melee weapons to begin with, they are ranged weapons. For the Thrown weapons that qualify, nothing in Monk does says that Martial Arts die only applies to melee attacks, so throwing a light hammer should still use the Martial Arts die and you can use Dexterity instead of Strength.
In the case of holding a non-valid weapon then yes, you can't use the martial arts die, but really, why would you? About the only time I think you would, it would be for making attacks outside of melee/thrown range.
One thing I do find fun is that under 2024, Monk technically now has proficiency in hand crossbow, probably some weird tactic somebody can think up with that one.