Details:
appt-now-displayed was set non-nil the first time a reminder was displayed.
Nothing ever set it back to nil again. Thus when full-check was nil,
mode-line-only was always true, so the "(when (or full-check mode-line-only)"
was pointless. That was the only use of full-check. mode-line-only
was only used in a negative sense, and can be reduced to the zerop test.