Why does plastic never dry properly in a dishwasher? Whenever I get tasked with unloading the dishwasher, I'm always amazed at the amount of water that's still stuck (always in droplets) to our plastic kitchen utensils and storage containers. 

We have a dishwasher with three racks, but it doesn't seem to matter which rack you use, plastic spatula's in the top cutlery rack, plastic containers or cups in the middle rack or our plastic cutting boards or plates in the bottom rack, all are equally wet when unloading the dishwasher, while the regular cutlery, glasses, metal pans and ceramic plates are all perfectly dry. 

Why do the plastic kitchen utensils never dry properly in the dishwasher? And is there anything that can be done so the plastic does dry in the dishwasher? (besides using a towel or just waiting three days before unloading)
In addition to the lower heat capacity (see other answer), a main reason, quite counterintuitive, why plastics don't dry well is that they're hydrophobic. That's right: they keep water sticking to them because they're water repellent (but not completely water repellent).

The reason for this strange behaviour is that any small amount of water on the surface of plastics immediately contracts to a compact droplet. This minimises contact with the plastic, but also with air, which is the problem: for efficient evaporation, you need a large air-to-liquid surface. You do get such a large surface on glass, ceramic and metal, because these are (at least when freshly cleaned) hydrophilic, so the water stretches out to a thin film coating a whole lot of the surface.

Not so with plastics. Only with some shaking will the droplets start running down the surface, and may combine with other drops and then drip off. With super-hydrophobic materials you'd be ok again because even tiny drops would immediately pour down, but most plastics are exactly at the sour spot: too hydrophobic for evaporation, but still not hydrophobic enough for a lotus effect.

Melamine resins tend to be among the better plastics in this regard, as they're still pretty hydrophilic. Still, they tend to dry only incompletely, probably because of the low heat capacity.