The newer more energy efficient dishwashers have moved away from heating elements which are just better at drying. Newer machines take longer to wash and don't dry as well in the name of energy efficiency. Current machines dry by heating up the stainless steel tub with hot water and using a rinse aid to have the water be better at sheeting off of your dishes. Your metal and ceramic items retain heat better than plastics, so if it's only your plastic items that are wet, that's just the way things are. If dishes or pots and pans are wet, then something could indeed be wrong.
I had so many problems with my LG machine - 2 different ones broke in 4 months... their customer support was terrible, too. I fought for and got a refund direcly from the manufacturer. I'm done with LG.