One of the dumb things I have noticed as far as "Upgrading" skyhold is those dumb notes on the large wooden preconstruction things. You HAVE to read them so they will be built like a catwalk or whatever.
"Construction Notes" have nothing to do with upgrading Skyhold. You read them for Codex entries, which grants you XP. My first playthrough, I didn't realize they were there and still managed to finish the game with Skyhold as upgraded as it ever gets.
Visually, Skyhold changes based on which quests you've completed. After you use the world map to travel somewhere once, the wreckage gets cleared from the main hall and the holes in the roof get fixed. After you complete the next major quest, Here Lies the Abyss or Wicked Eyes and Wicked Hearts, the scaffolding in the main hall goes away and tables move in. The stone rubble spilling across the lower courtyard gets cleared away (but the puddles remain). Once you've completed whichever you didn't do first, you get carpeting in the main hall, you are able to select a decor, and the scaffolding in Viv's balcony goes away. The last of the scaffolding is cleared from the stable area. The guest rooms off Viv's balcony are now accessible (I've got some great screenshots of Cassandra and my avatar taking a romantic stroll through the scaffolding...). The main hall is as full as it's going to get. There's always food on the tables, but you never see anyone sitting at them. I feel sorry for Skyhold's catering staff. The scaffolding in your quarters (and the Red Templar banner) never go away. You'd think the inquisitor would be able to order somebody to go up there with a broom.
I headcanon that the inquisitor mourns all the Inquisition soldiers who die because they never got moved to the infirmary, and that's why all the mirrors are covered, even after the end of the game.