I can confirm. When trying to open the Page settings dialog, an exception is thrown for "style is null":

ve.Element.js, line:

		top = parseFloat( loc ? style.borderTopWidth : $el.css( 'borderTopWidth' ) ) || 0,

Context:
ve.Element.getBorders = function ( el ) {
var doc = el.ownerDocument,

		win = doc.parentWindow || doc.defaultView,
		style = win && win.getComputedStyle ?
			win.getComputedStyle( el, null ) : el.currentStyle,
		loc = win && win.getComputedStyle ? true : false,
		$el = $( el ),
		top = parseFloat( loc ? style.borderTopWidth : $el.css( 'borderTopWidth' ) ) || 0,

Change 85692 had a related patch set uploaded by Krinkle:
ve.Element: Account for getComputerStyle returning null

https://gerrit.wikimedia.org/r/85692

Change 85692 merged by jenkins-bot:
ve.Element: Account for getComputerStyle returning null

https://gerrit.wikimedia.org/r/85692

Problem solved. Tested with Firefox 24.0 on Windows 7 64BIT.

Page-settings dialog is operational and working.

It's still happening, unfortunately. Ed found out it works fine on local and mediawiki.org, though.

TeamGale mentioned this today at en.wp:
<<Just wanted to ask...how can we add categories with VE? In the past I could do it by clicking on "Page settings" but now when I click on it nothing happens! Is there somewhere else a button that adds categories? I searched everywhere but I can't find it. If it's still on the "Page settings" then something is not working right... Thanks TeamGale 09:54, 3 October 2013 (UTC)>>

Fram tested as well:

<<Tested this. FIrst click on "page settings" gives no results. Second click opens the page setting window. But I can't do anything there.>>

I can confirm that the second click just launches an empty window, with only the "categories" label text on the left column.

<<Actually this one with the categories is happening for a while for me. Just when I first found it I was in a hurry and couldn't leave a feedback. Then I totally forgot about it till now that I needed to use it again. It's weird that no one else mentioned it here before though.
Elitre, I don't know if it's a cache problem but I'll try to clean my cache again and re-test it. But the "after a few attempts" is still not right for me. Shouldn't this happening in the first attempt? TeamGale 10:12, 3 October 2013 (UTC)
Update: Nop, still happening the same for me even if I clean cache, cookies etc... TeamGale 10:20, 3 October 2013 (UTC)
Hmm...it seems to be only a Mozilla issue. I just tried it with Mozilla on Greek WP and it still doesn't work. But when I tested it on Google, it was working just fine. TeamGale 11:00, 3 October 2013 (UTC)>>

Confirmed:

• Working on latest master locally (Chrome).
• Broken on mediawik.org (Chrome).

This should be fixed in https://gerrit.wikimedia.org/r/#/c/85692 , which is in wmf19 but not in wmf18. enwiki is being upgraded from wmf18 to wmf19 today, hopefully that'll fix it.

(In reply to comment #7)

This should be fixed in https://gerrit.wikimedia.org/r/#/c/85692 , which is
in
wmf19 but not in wmf18. enwiki is being upgraded from wmf18 to wmf19 today,
hopefully that'll fix it.

That's the patch that closed this bug (comment 3). But it appears there is indeed a new bug that causes the page settings dialog to be broken again due to an uncaught exception when the dialog is first created when clicking the page settings button.

It fails in Chrome like this:

Uncaught TypeError: Cannot use 'in' operator to search for 'scrollTop' in undefined load.php?…:102
vendorPropName load.php?…:102
jQuery.extend.css load.php?…:105
Tween.propHooks._default.get load.php?…:136
Tween.cur load.php?…:136
Tween.init load.php?…:135
Tween load.php?…:135
Animation.deferred.promise.createTween load.php?…:131
tweeners.* load.php?…:129
(anonymous function) load.php?…:130
jQuery.extend.each load.php?…:8
createTweens load.php?…:130
Animation load.php?…:132
doAnimation load.php?…:137
jQuery.extend.dequeue load.php?…:25
(anonymous function) load.php?…:26
jQuery.extend.each load.php?…:8
jQuery.fn.jQuery.each load.php?…:4
jQuery.fn.extend.queue load.php?…:26
jQuery.fn.extend.animate load.php?…:138
ve.Element.scrollIntoView load.php?ext.visualEditor…:11
ve.Element.scrollElementIntoView load.php?ext.visualEditor…:12
ve.ui.OptionWidget.setSelected load.php?ext.visualEditor…:404
ve.ui.SelectWidget.selectItem load.php?ext.visualEditor…:400
ve.ui.PagedDialog.addPage load.php?ext.visualEditor…:458
ve.ui.MWMetaDialog.initialize load.php?ext.visualEditor…:461
ve.ui.Window.onFrameInitialize load.php?ext.visualEditor…:353
oo.EventEmitter.emit load.php?ext.visualEditor.bas…:133
ve.ui.Frame.load load.php?ext.visualEditor…:351
ve.ui.WindowSet.open load.php?ext.visualEditor…:356
ve.init.mw.ViewPageTarget.onToolbarMwMetaButtonClick load.php?ext.visualEditor.bas…:87
proxy load.php?…:10
jQuery.event.dispatch load.php?…:45
elemData.handle.eventHandle load.php?…:38

Have split the new failure into bug 54928 and am re-closing this one.