Liz the Wizard is toe-to-toe with her foe, Joe. If Liz stabs Joe with a dart rather than throwing it, does she still get her proficiency bonus and avoid incurring disadvantage?
Using a dart like this makes it an improvised weapon, so no proficiency bonus
A melee weapon is used to attack a target within 5 feet of you, whereas a ranged weapon is used to attack a target at a distance.
In the weapons table on PHB 148, the dart is listed as a ranged weapon, not as a melee weapon with the thrown property. As such, using it as a melee weapon means you are improvising. From "Improvised Weapons" (PHB 147-148):
If a character uses a ranged weapon to make a melee attack ... it also deals 1d4 damage.
Unless you have a generous DM
However you might be able to apply your proficiency bonus, if your DM rules that a dart is 'similar to an actual [melee] weapon', a dagger maybe?
But in any case no disadvantage
Using improvised weapons doesn't automatically incur disadvantage according to the PHB.
(The DMG does suggest sometimes getting disadvantage when using improvised tools. This topic is dealt with in some depth in this rpg.se answer.)
Unless you have an evil DM
Though it's always up to the DM to impose disadvantage, so I suppose he or she might do anyway...
For more information on using a dart as a ranged weapon including ideas about what a dart might look like as a weapon see: What are the mechanics of using a dart as a ranged weapon?