42	+ // FIXME: Currently autopilot can only get visual items, but once it is
43	+ // updated to support non-visual items, a QtObject may be used.

Please add a link to http://pad.lv/1273956 so we know what you are referring to. Also, I find it useful to sign the FIXME comments, with something like --timp - 2014-03-19

637	+ current_tab = tabs.get_current_tab()
638	+ number_of_switches = 0
639	+ while not tabs.selectedTabIndex == index:
640	+ logger.debug(
641	+ 'Current tab index: {0}.'.format(tabs.selectedTabIndex))
642	+ if number_of_switches >= number_of_tabs - 1:
643	+ # This prevents a loop. But if this error is ever raised, it's
644	+ # likely there's a bug on the emulator or on the QML Tab.
645	+ raise ToolkitEmulatorException(
646	+ 'The tab with index {0} was not selected.'.format(index))
647	+ current_tab = self.switch_to_next_tab()
648	+ number_of_switches += 1
649	+ return current_tab

You should move this into a method. You can call it something like _switch_to_deprecated_tab_by_index

651	+ if (index != tabs.selectedTabIndex):
652	+ self.get_header().switch_to_tab_by_index(index)
653	+ current_tab = tabs.get_current_tab()
654	+ return current_tab

This is not a big deal, but it would also make it clearer putting those statements on _switch_to_tab_in_drawer_by_index

668	+ return false

Typo. It's False.

677	+ try:
678	+ tab_bar = self.select_single(TabBar)
679	+ except dbus.StateNotFoundError:
680	+ raise ToolkitEmulatorException(_NO_TABS_ERROR)
681	+ tab_bar.switch_to_next_tab()
682	+ self._get_animating().wait_for(False)

Same thing here ^

684	+ try:
685	+ tabs_drawer_button = self.select_single('AbstractButton', objectName='tabsButton')
686	+ except dbus.StateNotFoundError:
687	+ raise ToolkitEmulatorException(_NO_TABS_ERROR)
688	+ self.pointing_device.click_object(tabs_drawer_button)
689	+
690	+ tabs_model_properties = self.select_single('QQuickItem', objectName='tabsModelProperties')
691	+ next_tab_index = (tabs_model_properties.selectedIndex + 1) % tabs_model_properties.count
692	+
693	+ try:
694	+ tab_button = self.get_root_instance().select_single('Standard',
695	+ objectName='tabButton'+str(next_tab_index))
696	+ except dbus.StateNotFoundError:
697	+ raise ToolkitEmulatorException("Tab button {0} not found.".format(next_tab_index))
698	+
699	+ self.pointing_device.click_object(tab_button)

and here ^. Please wrap them in something like _switch_to_next_deprecated_tab, and _switch_to_next_tab_in_drawer

4	+ try:
685	+ tabs_drawer_button = self.select_single('AbstractButton', objectName='tabsButton')
686	+ except dbus.StateNotFoundError:
687	+ raise ToolkitEmulatorException(_NO_TABS_ERROR)

You can also move this ^

724	+ try:
725	+ tab_button = self.get_root_instance().select_single('Standard',
726	+ objectName='tabButton'+str(index))
727	+ except dbus.StateNotFoundError:
728	+ raise ToolkitEmulatorException("Tab button {0} not found.".format(index))

and this ^ into a private methods, as you have the same statements twice.

755	+class DeprecatedTabsTestCase(TabsTestCase):

I would prefer to do it with scenarios. Take a look at http://paste.ubuntu.com/7121301/
I haven't tried it, but something like that should work.

702	+ def switch_to_tab_by_index(self, index):

You are missing a test for this new method.

And some of your lines are too long. They will fail pep8.