We moved into a house recently and have discovered some less than good work that was done on the home. I am assuming this was done incorrectly as well but am not an expert and am looking for some input. The exterior door has no threshold on the outside, it is on the inside of the door sloping towards the inside. I have ants and water damage under the actual door frame as they did not caulk or use any type of protective membrane. I also noticed it is right on the edge of the exterior wall. Isn't that where a screen door should go and the actual storm door should be where that thick molding is that is 'framing' the door way? Do I buy a new door with frame and rip out that molding and move the door back?
Although the quality of the work may be questionable, it is an out swing door and the threshold is correct for such a door. Your recollection is of an inswing door, set to the inside face of the wall, out swings doors are set to the outside face.
The door perhaps was not sealed in with a bed of caulk and the weatherstripping does not meet in the corner. Simple fixes if you want to keep the out swing door. If you change the door to an inswing (regular) door, a reputable installer will fix all the issues you refer to.
This looks like a pre-hung exterior door assembly from a "big-box", designed to swing inwards as per normal, but installed backwards.
A good carpenter would have assembled jamb, threshold, and weatherstrip properly for the outswing scenario; it would not have come pre-assembled.
BTW, they make screen door sets for outswing doors (they swing inward by necessity) but they can't be found at the "big-box". And if you have room for a screen door to swing inwards you should just install a regular inward swinging door rather than the configuration that you have.
I am surprised to see an exterior door swing outwards as they typically swing inwards. One reason for this is as you mentioned how on earth will you install a storm (or screen) door and expect a decent result. Think about it for a moment - it makes it very difficult to get out of the house from the inside if there is a screen door installed and closed!
Basically it looks like a case of mistaken swing LH versus RH and then they installed the door backwards to make it work - probably a DIY'er (maybe they had no idea there was a such thing as left hand and right hand doors), I can't imagine a real pro doing it - but I admit I have not seen it all.
Check your building codes to verify if this is allowable, one reason someone might do this is that an exterior door that swings outward is much more difficult for anybody to kick the door in. A door that swings in, is much easier to kick in. If there are lots of break ins in the neighborhood perhaps your answer lies there.