Fan door does not close completely - Air Race Jet
I don't have this model.  Never built it, but thanks to Youtube we can understand with moving pictures the frustration, and build fatigue you might feel.

JANGBRiCKS says: 


  "It's one of those builds where you need to get everything exactly
  right the first time.  Penalty for making any sort of mistake is very
  very high and there are many things that are left incomplete for long
  periods time as you're building up the functions inside of this.  
  
  The main build of all of the gears, and all of the levers, all of the beams,
  and everything that connect together, ultimately, very very late in the game,
  late in the process of building to form the functions that are all
  powered by a single motor."



Think Loud's video review and speed build, is similar to your issue, where his fap door doesn't close properly, and he has to manually pop it down too.  So, I see what you mean, Bro. 



I'll take your word that all connections are good, so we're not gonna think it's, an 


  "artifact of a mistake elsewhere."


(Luv how you said that!)

So, in trusting you, I think your build is right instruction-wise, but our engineering insight could use a slight twist here and there.

So, in this Vertical Take-Off and Landing mode, we see:


Top blue flap comes up.
Two bottom blue flaps spread open.
Rear gray exhaust nozzle drops down.
Two black flaps on back of wings that turn down.







For all of these features to work properly, you have to go back to your build, and manually turn each section, or gear torque completely to position "0" of VTOL mode.

So, if one or more is off, even slightly, it will affect the total length of deployment, and retraction of the others.  

I can only imagine one of the features positioned too early hitting a physical wall, or space constraint, causing the other features not to fully complete their run.   

You did mentioned the top gap, bottom gaps, and misaligned tail engine. Yes, they're all related to the VTOL feature so, if one is off, they're all gonna be off.

Try this out, and hit us back with your results. 



My source videos:


LEGO instructions - Technic - 42066 - Air Race Jet. by LEGO
instructions - Fan - Site.
Lego Technic 42066 Air Race Jet - Lego Speed Build and Review by
Think Louder.
LEGO Technic Air Race Jet 42066 review! by JANGBRiCKS.