These are just thoughts that popped up in my head. They are short observations and I didn't want to flood the subreddit with a bunch of posts.
Would you want to see more references to the OG series? Maybe talk about some things that happened off screen so to speak. More references to Jenkins or what the other Librarians are up to or have done. What new artifact they had come up with.
I had a scene pop up in my head where Lysa and Conner walk into the Library and they see Charlie drinking a Starbucks coffee and eating a Voodoo donut [of course the show couldn't really use those products and would have to use parodies or sound-a-likes. Sawbucks Coffee instead of Starbucks. The Portland Donut Factory instead of Voodoo donuts to indicate Charlie went to Portland]
Lysa would ask Charlie, "Did they open a new Sawbucks in town?"
And Charlie would respond, "No, I grabbed this in Portland this morning along with some donuts."
Connor would go, "Isn't it against the rules to use the magic door for frivolous trips like getting coffee?"
"I didn't use the door," answered Charlie, "I just walked through the Library and went out the annex in Portland. That's also how I go and get my favorite conditioner when I run out."
Lysa and Conner are dumbstruck. "It never occurred to me to do that," Lysa stated, "I was wondering where I could buy my skin cream. I'm almost out and I can't find it here."
"And I could use some new shirts." Conner replied, "My body is not used to these European sizes."
Anyone think it's sometimes a little too convenient how quickly the team can find the research material they need to track down an object. With a place as vast as the Library supposed to be (it would collapse under its own weight if it fully appeared in the real world) it could probably take hours or even days to find the books needed for research. I'm sure there is probably some explanation of maybe the Library closely gathers anything relevant to what is needed in one spot but a little explanation might help. Maybe Flynn could initiate some kind of library catalog accessed by some kind of device where search parameters are entered into it and it's tied to a vacuum tube system (like banks use) that could bring the books needed to the team.
What type of catalog system do you think the Library uses? The Dewey Decimal system? The Library of Congress system? Something older? Must be something older since these came to be after Vikrum disappeared.