Fixed the missing sub-areas in the next release. Integrations were only showing sub-areas for the first integration on the page. This was due to reusing the same ID pool for sub-area integrations.
Also fixed the inconsistent avatar type in forum-list integrations. It appeared to be random, but was possibly related to whether the user was already listed elsewhere on the page.
With the counters, it does not appear to be a math bug since the numbers appear to also be wrong in your database. It is important to know that the counters are not counted on demand. They are incremented with +1/-1 as books, etc are added or deleted. If there is a bug, it involves a +1/-1 that should have happened, but did not happen, or possible +/- that were double-counted. Since the numbers are so far off, it would need to be a massive event (such as deleting 300 books at once, or moving 300 books to another area, which you would probably remember), or occurred gradually over time (a long period of time if the number is that far off). For a gradual counting problem, it could be that the bug was fixed but we didn't recount all the content at that time. So the question is whether the counter is correctly changing now. If you create a new book, does it +1; if you delete, does it -1?