So I am starting a list of all the known cut content in the game that I at least know of
Cut quests
-20 Leagues under the sea
-At a Minutes Notice
-Looking to the Future
-Off the Grid
-The Enemy of my Enemy
-The Replacement
All of these were found via the pipboy app being data mined, and yet aren't in-game.
However, from what I've seen/gathered from Fo4edit, and the data-mined pipboy app.
-At a Minutes Notice appears to be a prototype version of the "When Freedom Calls" MQ, it uses the same icon.
-Looking to the Future appears to be a prototype version of the "Mass Fusion" quest. It uses the same icon, except a normal pipboy instead of one in power armor, suggesting that at one point The Institute's version of the quest may have been a separate one from the BoS's, that they just merged down into one quest where you could pick a side.
-The Enemy of my Enemy appears to be a cut/prototype version of the "Dangerous Minds" MQ, where you explore Kellogg's memories. All the dialog between Piper and Nick about going to Memory Den to get Kellogg's brain scanned and whatnot is still listed under that quest in Fo4edit.
Cut weapons include
-Chinese assault rifle
-Harpoon gun
Mis cut content includes
-Cut data found via fo4edit suggests that at one point the player was supposed to fight Cait in the Combat Zone, and was able to play bets there arena style.