Old collections demonstrate a lack of professionalism as much as a lack of funding. It costs nothing except an hour or so a week to weed out old materials. Each week pick one section of bookcase and look at each book. If it is less than ten years old or has been checked out within the last three years, keep it. If not, toss it. Dump duplicate copies unless popular. Toss anything that is worn-out.
When people started talking about the "Long Tail," I asked myself, "OK, if Amazon's the Long Tail, what's the Short Tail?" Thinking like this is a 21st Century Skill. My answer to myself was "a school library."
Let's pause for a moment to note that this does not represent a criticism of school libraries, but an attempt to help you understand the concept of the Long Tail. Thank you for not freaking out.
Because in many or most school libraries, the not very carefully maintained ones, and probably particularly high school libraries, you've got some books that are checked out constantly, a block that are checked out a couple times a year or so, and many, many books that are likely to never be checked out or read again. You've got a short tail, whether or not you keep the books on the shelf or weed them. It would be a Long Tail if everything was checked out occasionally, and you'd have a Long Tail business model if keeping all those rarely read books around was cheap enough that you could still make money off very rare use.
What's the difference? Compared to Amazon, or a public library, you've got a small pool of people using a school library. I would guess that a lot of books in a school library go stale quickly -- kids probably don't want to read middling young adult fiction from 1995 or 1985, moreso than adult fiction -- and a lot of the science and reference books get out of date quickly. Areas not covered in the current curriculum would be left behind.
The other side of the equation is that the cost of keeping books in the school's collection is high, particularly compared to Long Tail businesses that only store and ship bits. Those extra books in the school collection take up space, as Doug points out can make it harder to get money for new books, make it harder to find books, and generally have to be maintained.
So... school libraries are short tail. Not that there's anything wrong with that!