What parts needed to finish exterior door?
If this was an interior door I would say just live with it but since it is an exterior door I think you need to have it reinstalled.  

Issues:


The biggest is that the threshold should be at most a minimal bump to your house.  This is just odd and a tripping hazard.  There is really no way to fix this.  You in theory could cut off the head of the threshold but...
The gap underneath the door is just way too big.  So even if you could cut a 1/2" off the threshold, this would just make your issue worse.  You can install an extension on the door here and they make some great rubber ones that will form to the gap but this doesn't look great even if it works.  And this gap at the bottom is just inviting all bugs in your area into your nice home.
The gap on the bolt side is way too big.  You can add weather stripping but it will require so much that it won't look great.  Also since this is the opened side you will be replacing it constantly.  I don't want to focus on this too much but with a gap that big it would be pretty easy (by force or pushing lock) to open from the outside.
The door isn't true.  A slight slant will eventually have even more issues and may compound the other 3.


If I were to guess this guy left some of the existing "subfloor" under the door frame.  And it probably wasn't even.  This jacked your frame up higher.  Which means the sides are higher... The threshold was installed too high too.   The thing about this is there isn't a fix.  If there is, it is shady and ruins other aspects of your house.  You have one glaring problem, the door is installed wrong.  Take off the trim, cut out the door and have it reinstalled.  A good handyman can have everything back together in 2-3 hours max.