I'm going to remove the KNOWN BUGS section of whic-func.el. AFAICS, both problems have been fixed.
;; KNOWN BUGS
;; ----------
;; Really this package shows not "function where the current point is
;; located now", but "nearest function which defined above the current
;; point". So if your current point is located after the end of
;; function FOO but before the beginning of function BAR, FOO will be
;; displayed in the mode line.
;; - If two windows display the same buffer, both windows
;; show the same `which-func' information.
As for its TODO-LIST item 1, it seems like this package should perhaps profit from new technologies?
;; TODO LIST
;; ---------
;; 1. Dependence on imenu package should be removed. Separate
;; function determination mechanism should be used to determine the end
;; of a function as well as the beginning of a function.
;; 2. This package should be realized with the help of overlay
;; properties instead of the `imenu--index-alist' variable.