On Sun, 16 Feb 2014 14:16:30 -0800 (PST), Greg Rodenhiser
wrote:

The trim corner referenced (I believe in the same picture showing the air/light gap is on the inside of the house... The outside trim is all vinyl and appears tight. The rail I'm mentioning is the adjustable wood rail of the threshold that sits under the door...

I've always had storm doors. Never had entry doors exposed to
rain/snow.
I suggest you install storm doors.