When working on bug #740574, I found out a bug that turned out to be present even without applying my patchset.

(nm-applet:20586): GLib-GIO-CRITICAL **: g_loadable_icon_load: assertion 'G_IS_LOADABLE_ICON (icon)' failed
(nm-applet:20586): Gtk-WARNING **: Error loading theme icon 'gtk-connect' for stock: Failed to load icon
(nm-applet:20586): Gtk-CRITICAL **: render_fallback_image: assertion 'pixbuf != NULL' failed
(nm-applet:20586): GLib-GObject-CRITICAL **: g_object_ref: assertion 'G_IS_OBJECT (object)' failed
(nm-applet:20586): Gdk-CRITICAL **: gdk_cairo_surface_create_from_pixbuf: assertion 'GDK_IS_PIXBUF (pixbuf)' failed
(nm-applet:20586): GLib-GObject-CRITICAL **: g_object_unref: assertion 'G_IS_OBJECT (object)' failed
(nm-applet:20586): GLib-GIO-CRITICAL **: g_loadable_icon_load: assertion 'G_IS_LOADABLE_ICON (icon)' failed
(nm-applet:20586): Gtk-WARNING **: Error loading theme icon 'gtk-connect' for stock: Failed to load icon
(nm-applet:20586): Gtk-CRITICAL **: render_fallback_image: assertion 'pixbuf != NULL' failed

I found the exact lines of code that, when removed, also remove the warning.

if (active) {
    image = gtk_image_new_from_stock (GTK_STOCK_CONNECT, GTK_ICON_SIZE_MENU);
    gtk_image_menu_item_set_image (GTK_IMAGE_MENU_ITEM (item), image);
}