I agree with the idea that "inactive users" really doesn't need to be there. I would expect to find that "sample of most recent inactive users" at the bottom of the first page shown in "Users and Groups" tab, rather than the bottom of "General". But that might be more important on boards with admin approval.
The "Resynchronise or reset statistics" section seems about as good a place as any to have it. I agree that I've never used anything except the "Purge Cache" out of that list. But I wouldn't want to arbitrarily "scatter" or hide those other options somewhere else. Having these options right under the "Board Statistics" display seems like a logical place to have them.
One option perhaps missing there could be "resynchronize all forums"? i.e The equivalent of going to the "Forums" tab and hitting the "sync" button on each one in turn. Not that I have personally needed to use that; just perhaps something logically missing from "Resynchronise or reset statistics".
"Logged administrator actions" is important enough that it needs to stay, although I would say I don't typically refer to that. In addition to that, or in place of that, I would have actually liked to see "New errors logged since last ACP visit" or similar. Errors I didn't expect were happening seems more important than the possibility of rogue or unexpected admin actions; although both are important.
"A configurable list of links" sounds fine, but I don't think I would bother configuring it. Instead I would just go click in the section of the thing I would link to, if the link wasn't already there.
"Saving screen real estate" on this summary page does sound possibly beneficial? Meaning instead of being able to configure links or remove links, what if in the "Resynchronise or reset statistics" section we took a Microsoft Office-like "only show recently used menu options" approach. i.e. Most people would end up with a section that shows only the "Purge Cache" link because that's all we use, and a "show all options" link to reveal the rest of the lesser-used links. Maybe the "show all options" link displays as "hide unused options" when showing all, as the way to opt-in to showing less.
Being able to order the sections maybe could be part of that answer too. e.g. Being able to move a summary of the recent Error log entries to appear above the summary of recent Admin log entries might be preferred by some. And maybe even moving it to appear before the "Resynchronise or reset statistics" section. Just the same "draggable/collapseable sections" want that some have for the main forum display, too. That seems overly complicated for such a rarely used page though; if we simply have "two log summary sections" and I could choose whether Errors or Administrators was in the first and second instance of it, that would be plenty of configurability in my mind.
Random ideas: What about saving a snapshot of the statistics each visit, and above the "Board Statistics" section have a drop-down with entries like "Current", "Five days ago", "One week ago", etc. And when you select anything besides "Current", the "Board Statistics" shows the current numbers but with a "+185 (8%)" type display beside each number that has increased or decreased, to show how much change occurred since the selected time. I'm lazy and don't want to say "create a cron to guarantee these snapshots are available" (that would be fine too, though), and would simply save a snapshot whenever ACP was actually visited. So what's available in the drop-down would vary depending on how frequently you visited.