What makes you think the library's construction was faulty? What you describe sounds fine. But it doesn't say anything about whether the library is "problematic".
When building the library, the most important thing to keep in mind is your players. Give them the Arts and Abilities, and spells, you want them to be able to have easy access to. Don't give them what you want them to work hard for, or even trade for, in-game. Don't just give the players what the characters would want the library to have.
So... does your library do that? Do you want your magi to have access to that Q10 L14 summa on Perdo? Having it around means that a starting specialist in Perdo will (probably) find it useless, but others could catch-up to about his level relatively quickly (in about 10 seasons, or less). Is that what you want? What about the other Arts? Have you, for example, considered whether you want Roots (Q15, L5) in Creo and Corpus, so that magi could learn healing magic? Perhaps also Ignem, and complement that with a Pilum of Fire lab text for basic combat competence? Or perhaps Rego Vim and a low-level Aegis of the Hearth, to make sure the covenant can whip-up an Aegis?
Of course, there is no need to fess over every choice. It's perfectly fine to just throw some "random" stuff in; just make that stuff doesn't include undesirable works.
If you enjoy figuring out the history of the covenant's library, by all means do so. ArM is a game, and games are for fun. But keep what you want the library to become in mind. It need not become so organically - a fire can chip away some "undesired" books, trade can bring in ones that there is no rationale for making locally, and so on. Do have fun constructing the library, but also make sure it serves the needs of your saga.
And don't forget that a library can pile up lots of lab texts, including some rather useless ones ("why Magus Nicratoxos thought the library should include his notes on how to make a black-goat shaped bronze statue that breathes poisonous gas is anyone's guess...").
Finally - what about all the other books? Consider what Abilities you want your characters to have access to easily - Area Lore? Order of Hermes Lore? Penetration? Finesse? Parma Magica, even, perhaps? What about spell mastery? What about Leadership? Charm? Intrigue? Or Hunt? Brawl? Swim?