Do you remember you will focus also on post processing of HDRI images after rendering? :-) .
It makes the render then overall more real looking....if you dont mind I tried again one really by a few seconds of work.
??? I don't know what kind of "post processing" do you want to perform on HDRI images but what I can see on your picture are totally lost details in dark areas of your background = bad "photo".
Easily fixed with smoothing groups Grudd.
In the modify menu on element level (the little cube), scroll down and just assign the faces that have the problem to another smoothing group. In this case it's probably the door line. So select it (it's one element) and then change the smoothing group and it should fix it.
2.. not so "quickys" if you will
obviously you can tell in the second picture that there is a good amount of light artifacting on the spoiler.. i'll have to work on that, not completely sure why after it did so after all i've done.. owell