A spin-off question from an earlier post, can you two-weapon fight with a dart or other thrown ranged weapons?
Two-Weapon Fighting
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
–PH page 195
Assuming you have the dual wielder feat which allows you to ignore the "light weapon" clause.
I read the second paragraph to mean that if the melee weapon has the thrown property you can throw the melee weapon.
However, another RPG.SX user reads it as if the weapon has the thrown property, you can throw the weapon, melee or not.
Best Answer
From the rule you quote:
Which weapon(s)?
So the weapons of "either weapon" mention are the light melee weapons from the previous paragraph.
You can't throw both darts, because they're not valid weapons for two-weapon fighting.
And neither is a melee weapon, so:
You can't make improvised (dagger?) melee attacks with both.
But doesn't using a dart as an improvised dagger make it a melee weapon? "Improvised Weapons" (PHB p.147-148) says "in many cases, an improvised weapon is similar to an actual weapon and can be treated as such." (emphasis mine)
Nope. Later in "Improvised Weapons" we have "if a character uses a ranged weapon to make a melee attack...." (emphasis mine) The authors could have said "ranged weapon as a melee weapon" or something that indicated some change in the weapon's type, but they didn't.
It's still a ranged weapon, per the table, even when used to make a melee attack.