Diagnosis
The heating element that dries the dishes at the end of the cycle (the "Dry" phase) might not be coming on, or you're using an eco/energy-saving cycle that skips the heated dry to save power.
How to Fix It
First, check your cycle selection. Cycles like Eco or Delay Start (depending on settings) often use condensation drying only, which leaves dishes wetter. Run a Normal or Heavy cycle with the Heated Dry or Sanitize option selected—these force the heater to run. Also, ensure your rinse aid dispenser is actually dispensing; the little float in the dispenser door can get stuck.
If That Didn't Work
If you're sure you're using a heated cycle and still get no heat, the heating element or its high-limit thermostat might have failed. You can sometimes check this by running a cycle, then carefully feeling the lower part of the door (where the vent is) near the end of the cycle when it should be in Dry mode—it should be very warm to the touch. If it's cold, the heating system has an issue.
Heads Up
Plastic items will always be wetter than ceramic or glass—that's physics (they don't retain heat as well). For better drying of plastics, use the top rack only and make sure you're loading dishes so water can drain off them, not pool in cups or bowl bottoms.