Thanks Demon,To the O.P I apologize but By the time the pix were sent I was wrapped up in a thing called roofing.
Pic 1- Looks like at your time of roof replacement your roof had 2-3 layers.At one time there was a leak and someone put some silly cone on the J channel where it meets the shingles.
The J is pretty high off the roof deck but other than your roofer not cleaning the J its not really his problem as long as he made you aware of the height difference from the J to the roof deck prior to roof replacement.That’s truly typical with multiple roof replacement.
The siding is scuffed from the tear off.Karnak and Tamko as well as others make a product that remove those scufs from the siding/J channel…That should have been cleaned before the job was considered “Complete”.
Also the siding installers cut the J channel wrong and some of the siding is cut @ the wrong angle.Hopefully they installed new step flashing @ the wall.Reroofs IMPO should have every component on the roof system replaced with new.
The drip edge has an inappropriate wrap/cut transitioning from one gutter line/angle to another.Your fascia wrap has an improper wrap.If the transition from one fascia to another is not wrapped with fascia wrap your installers should have at least putt a corner/butt cap on it.You should have had an apron for the slope where it meets the wall.
Pic 2- That external flashing thing looks like crap.As its been indicated the correct installation IMPO is for each INDIVIDUAL shingle should have its OWN piece of step flashing.
I am not real happy with the height of the corner post but once again if your contractor made you aware of the height difference then its not his problem.Corner posts that are high off the roof deck as yours is ,well that indicates multiple layers.
The nail head below the corner post is pointless but nonetheless should have been sealed.IMPO the aprons should not have nails blasted into it.Its very simple to make clips that are fastened under the apron and flipped over the apron eliminating exposed fasteners.They should have sealed the nail heads.
I think that deuce (2) elbow off the down spout that goes into the gutter looks like pooh.A single bend elbow is what’s needs.The water has to have as much ability to travel down un abstructed as possible.
That gutter elbow that comes out of the gutters is absolutely insane.It going out and over the gutters.That one is not even in the gutter but up and out.I can say this though,Thersi is no way that siding was installed after roof replacement.