Following comments to this question, the issue described below is probably a recent bug that might affect the badge count of all users on all sites. Thus, much of my original question is probably not related to the root cause of this particular bug. Or maybe it is, you never know.
Today, to my surprise, I was awarded the Taxonomist badge on Stack Overflow. That was unexpected because I don't usually create tags there (but when I do, they're renamed in the next fifteen minutes).
To my even greater surprise, that badge did not reflect in my silver badge count, which remains stuck to
22 instead of the expected
23 (and I counted that twice... thrice... four times now).
Initial investigations on meta led me to Wrong Badge Count, and at first glance it explained the issue because I didn't believe the badge to actually be legit. However, further digging revealed that award is actually a side effect of one of my first edits on SO (I wasn't even realizing I was creating a new tag back then) and is perfectly legitimate after all.
Are there badges that do behave this way, and if so, which ones? Is there a legitimate reason for them to do so, or can they be fixed?