Dewey and Della sing a small portion of the song "Stand Out" from A Goofy Movie (1995) whilst on their way to the vault.
The code to the vault is shown to be the first few lyrics to The Spectrum Song in An Adventure in Color/Mathmagic Land (1961) (red yellow green red blue blue blue red purple green yellow orange red red), which was the TV Special that Ludwig Von Drake made his debut in.
One of the doomsday scenarios that Ludwig mentions in his video message involves the Earth being taken over by "hyper-intelligent hairless apes"...in other words, human beings.
The Echo Base from Star Wars: Episode V - The Empire Strikes Back (1980) can be seen in the background just before Scrooge notices his plane is gone.
The Doomsday Vault is based on a real life institute: the Svalbard Global Seed Vault, located in Norway and established by Cary Fowler in 2006.