Sharp Plastic, when it's not supposed to be there. The only note that I know of which can naturally smell like plastic is probably almonds. But it's generally anything that doesn't feel very refined, or smells too sharp. A fragrance being synthetic is more of an impression rather than an accurate description. Personally whenever a fragrance feels harsh as it transitions through its' notes I describe it as synthetic, as opposed to being smoothly blended. Let's say a fragrance is supposed to smell like a dry cup of coffee, if it smells just like that it's not synthetic. If it smells like a sharp cleaning product plus coffee it's synthetic.
Of course there are synthetic fragrances that smell very smooth and vice versa.