Hello,

The recent changes on the compilation-in-progress indicator[1] made me
realize that the indicator lingers in the mode-lines of some windows.
To reproduce from emacs -Q:

    C-x 2
    C-x 2
    M-x compile RET C-a C-k true RET

"[Compiling]" correctly disappears from the current window and the
compilation window, but it lingers on the mode-line of the third window.

The attached patch trivially fixes the issue; I do not know whether it's
appropriate, or maybe too heavyweight.