Something I discovered recently is that the "progress to next badge" tracker is visible on the "activity" tab of other users' profiles (showing whichever badge they've set as their next badge to be aiming for). This feature makes it possible to see your badge progress for a consecutive-days badge while logged out. (You can't use the consecutive-days count in your profile, the better-known place for it, because that isn't visible while logged out.)
I've been intentionally trying to avoid the Enthusiast/Fanatic badges, so I take a day away from Stack Exchange every now and then to reset them. Previously I did this by just counting the day manually, but it struck me that this indicator might be an easier way to see when the progress reset. After not logging into Stack Exchange for several days, I began to suspect that something was up.
It turns out that as long as you don't log into your account, the badge progress on Enthusiast and Fanatic freezes in place (thus showing a misleading value, as actually logging in will reset it to zero).
The most obvious fix I can think of to this situation is simply to hide badge progress except when viewing your own profile when logged in; this has already been suggested by another user on the basis that it's a privacy leak (as badge progress isn't always visible by other means). Another argument against it is that as it relies on the "next badge" setting made by the user in question (while logged out, you can't change it to inspect the progress from other badges), any potential use of it would be somewhat inconsistent (most people don't think of their "next badge" setting as being one which has effects on other people, and thus you're effectively being shown one particular badge progress report for the user in question chosen in an arbitrary manner). Given the comparative uselessness of the feature – and the way it makes some users uncomfortable – removing it may make more sense than going through the effort to fix bugs in it.
If the count is to be shown, though, it should at least be accurate.