Unlike a warm outlet or a flicker, a burning or "hot plastic" smell near electrical equipment should be treated as urgent every time.
Loose or corroded wiring connections generate heat as current passes through them, and the insulation or plastic fittings nearby can start to smell before any visible damage appears.
A circuit carrying more current than it's rated for over a sustained period can heat up cabling insulation, particularly in older homes with undersized wiring for today's appliance loads.
Sometimes the smell is coming from a specific appliance rather than the fixed wiring itself. Unplug anything nearby and see if the smell persists.