The failure in my charger was pretty significant, so I'm not sure it's something that would happen slowly.
The car itself has insulation monitoring circuitry that will detect a short to chassis, so it's pretty unlikely that anything is damaged that badly if the car still drives and charges normally.
2011 Leaf? If so, you should be able to pull up the rear seats and see the charger. If the smell is really bad at that point, then it might be worth starting to plan for a replacement charger...
If there's no more smell there, I wouldn't worry too much and just keep using it.