1.exposed nails needs to be caulked
2.upper corner of skylight might need to be reshingled,so apron peeks on bottom part of shingle if its velux,if just all soldered single piece skylight then solid bead of caulking all around skylight.
3.vycor probably was applied ebcause installer thought it might give extra protection ,underneath there should be aluminum flashing,which is more than enough to hold it waterproof.
4.ridge vent ending is bit off,but nothing to worry about.
5.counterflashing looks correct except using clear caulking instead of fresh mortar.But its ok for 5-20 years.Depends on silicone type.
6. felt paper under ridge vent is probably just a single piece wasnt cut and left hanging.nothing to worry.