Yesh, not sure how I missed that earlier.
Iron Man - Usage of the S.H.I.E.L.D shorthand hadn't come into usage until some point off screen during these events
Avengers - Fury claimed that Thor was the reason for Phase 2 and that they hadn't been aware of Aliens until him.
Avengers 2 - eats a sandwhich cut diagonally. You can chalk this up to semantics or possibly an actual plot point though.
Winter Soldier - Fury had both eyes when he was sworn in as director of S.H.I.E.L.D.
Pierce, Cap, and I believe Maria all use Nick when referring to Fury so that little spiel in CM also has no basis in the other films.
Again, nothing earth shattering but when you put them all together it just makes it feel like the writers didn't even bother to watch any of the other films especially when a few minor script tweaks could have handled most of this.
Iron Man 1 - The long form of SHIELD is literally a joke line, it's there to make comic book fans think "oh em gee, SHIELD is in this!". It doesn't take a genius to abbreviate the organisations name. Also, Coulson's character is/has always himself been jokey, he was joking when he said "we're working on it" in reference to making the name shorter.
Avengers - Fury is the director of SHIELD, do you really think that he is going to tell 2 lower level SHIELD agents and 4 people he doesn't know about the fact that he has come across aliens? At the end of Iron Man he says to Tony that he is part of a much larger "universe", why would he say that specific word? Also, SHIELD has had dead alien bodies in storage for years, it's how Coulson was brought back to life.
Avengers 2 - Cmon, it's literally a joke about a sandwich.
Winter Soldier - You're right about this one, not sure why this was hand waived away.
As for people calling Fury by the name Nick, I can't remember if they specifically call him Nick directly to him or if they just say Nick in reference to him. If they do say it directly to him, Winter Soldier takes place nearly 20 years after Captain Marvel. Maybe he stops caring about being called Nick.
Some mental gymnastics maybe, but no more than the mental gymnastics required to come up with the "inconsistencies".