Check that the condenser fan under the unit is running.
If it has one.

Also check that the vents under the unit are clean.

If your drip tray sits over some condenser coils make sure they are clean.

For the interior moisture check that the door seal is clean and sealing properly all the way around the door.
On the hinge side sometimes the seal catches on the frame, to solve this give it a light coat of white lithium grease or vaseline.

It could be that the unit is creating so much moisture that the drip tray cannot keep up.
You may want to check the interior temperature, perhaps it is too cold and is generating too much condensation. It should be 40 degrees F.

Note: Some units have an energy save switch if your unit has this turn it off.