If you don't already do so...work in the branches. That's it. Seriously. That's my only suggestion - work at least - AT LEAST - one day a week/fortnight/month in a branch library.
Why? Practical experience. Nothing beats it. And maybe it'll give you some insight as to why staff are skeptical about new policies, revised policies, ditching old policies, events or activities that do nothing to promote collections, pricing changes and everything else in between.
I never want to forget how to check in/check out a book, shelve and/or talk books with customers and answering reference enquiries. What I could have done without, as a library assistant, are purchase orders, banking, quarterly reports, rosters and even training staff.
Query: would an admin assistant per branch alleviate a lot of the non-core chores such as those listed above?
Answer: dunno, but I like the idea of it.