The moisture you are seeing is probably from the defrost cycle.
It should drain out a hole below the evaporator coils at the back of the freezer and then down into the drip tray under the unit. This water then evaporates.

I looked at the Sears parts site but could not see exactly where this drain is.

I would check that it is clear.
If plugged a turkey baster with warm water, an air compressor with low pressure or a wire can often be used to clear it.

Also check that it is not plugged with dust etc. at the drain pan end.
You might as well clean the condenser/compressor fan and the condenser coils while you are down there.

If it looks like stuff is growing in the tube I would flush it with a 10% bleach solution. This should kill the stuff and let you flush it out. You may have to do this several times, let it sit for 15 minutes or so between flushes.

Be careful that the drip tray does not overflow and empty the drip tray after you are done.

Be sure to unplug the unit while doing this.