When exiting Gedit 3.12 there's a Valgrind warning:

==20156== Invalid write of size 8
==20156==    at 0x7704675: g_nullify_pointer (gutils.c:2030)
==20156==    by 0x744CBEE: weak_refs_notify (gobject.c:2572)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5649937: gtk_box_forall (gtkbox.c:2557)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x56498EE: gtk_box_forall (gtkbox.c:2541)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x56498EE: gtk_box_forall (gtkbox.c:2541)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5779D5B: gtk_overlay_forall (gtkoverlay.c:552)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==  Address 0x114c1030 is 16 bytes inside a block of size 184 free'd
==20156==    at 0x4C2B68C: free (in /usr/lib/valgrind/vgpreload_memcheck-amd64-linux.so)
==20156==    by 0x746AB79: g_type_free_instance (gtype.c:1932)
==20156==    by 0x5893791: gtk_widget_real_destroy (gtkwidget.c:11516)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x57973E8: _unmanage_popover (gtkpopover.c:1461)
==20156==    by 0x76C1A7F: g_hash_table_remove_node (ghash.c:448)
==20156==    by 0x76C2039: g_hash_table_remove_internal (ghash.c:1300)
==20156==    by 0x5797697: gtk_popover_update_relative_to (gtkpopover.c:1496)
==20156==    by 0x57990C6: gtk_popover_dispose (gtkpopover.c:212)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5755392: gtk_menu_button_dispose (gtkmenubutton.c:1024)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5649937: gtk_box_forall (gtkbox.c:2557)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x56498EE: gtk_box_forall (gtkbox.c:2541)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)
==20156==    by 0x5694480: gtk_container_destroy (gtkcontainer.c:1410)
==20156==    by 0x7448F91: g_closure_invoke (gclosure.c:768)
==20156==    by 0x745B7C3: signal_emit_unlocked_R (gsignal.c:3667)
==20156==    by 0x7463448: g_signal_emit_valist (gsignal.c:3307)
==20156==    by 0x7463701: g_signal_emit (gsignal.c:3363)
==20156==    by 0x588DEB7: gtk_widget_dispose (gtkwidget.c:11348)
==20156==    by 0x744F97F: g_object_run_dispose (gobject.c:1073)

Also, sometimes Gedit crashes on exit, and I suspect this is related to the Valgrind warning.
Also, Gedit bug 726673 (Crash when closing gedit) might be the same problem.

I think the Valgrind warning is related to GtkPopoverAccessible (when removing all popovers from Gedit source code the Valgrind warning disappears).
It looks like GtkPopoverAccessible adds a weak reference (with g_object_add_weak_pointer()) to the GeditStatusMenuButton which it is relative to. But on exit the GtkPopover is destroyed before the GeditStatusMenuButton is; but GtkPopoverAccessible doesn't remove the weak ref from the button.
So when the button is destroyed, it still has the weak ref to GtkPopoverAccessible, and tries to null it; but the memory location it tries to write to was in the private data of GtkPopoverAccessible and is already freed it seems.

This happens with Gedit 3.12 and Gtk 3.11 (both from recent jhbuild), under Ubuntu 14.04 x86_64  in Virtualbox.