Attached is the full stack trace.
When I re-submitted the form a few minutes later at 19:20 it failed again, this time saying the page was already deleted at 19:08, so apparently the error was fatal, but deletion did succeed internally.
2013-05-20 19:08:26 mw1179 mediawikiwiki: [4cc7abf7] /w/index.php?title=Thread:Project:Support_desk/no_respond_to_any_clicks/actions.&action=delete Exception from line 982 of /usr/local/apache/common-local/php-1.22wmf4/extensions/LiquidThreads/classes/Thread.php: Post 27727 has contaminated reply 27729. Expected 27727, got 27694
#0 /usr/local/apache/common-local/php-1.22wmf4/extensions/LiquidThreads/classes/Thread.php(996): Thread->checkReplies(Array)
#1 /usr/local/apache/common-local/php-1.22wmf4/extensions/LiquidThreads/classes/DeletionController.php(45): Thread->replies()
#2 /usr/local/apache/common-local/php-1.22wmf4/extensions/LiquidThreads/classes/DeletionController.php(48): LqtDeletionController::recursivelyDeleteReplies(Object(Thread), 'Parent thread d...')
#3 /usr/local/apache/common-local/php-1.22wmf4/extensions/LiquidThreads/classes/DeletionController.php(27): LqtDeletionController::recursivelyDeleteReplies(Object(Thread), 'Parent thread d...')
#4 [internal function]: LqtDeletionController::onArticleDeleteComplete(Object(WikiPage), Object(User), '[[Extension:Liq...', 125772, Object(WikitextContent), Object(ManualLogEntry))
#5 /usr/local/apache/common-local/php-1.22wmf4/includes/Hooks.php(196): call_user_func_array('LqtDeletionCont...', Array)
#6 /usr/local/apache/common-local/php-1.22wmf4/includes/GlobalFunctions.php(3834): Hooks::run('ArticleDeleteCo...', Array)
#7 /usr/local/apache/common-local/php-1.22wmf4/includes/WikiPage.php(2642): wfRunHooks('ArticleDeleteCo...', Array)
#8 /usr/local/apache/common-local/php-1.22wmf4/includes/Article.php(1635): WikiPage->doDeleteArticleReal('[[Extension:Liq...', false, 0, true, '')
#9 /usr/local/apache/common-local/php-1.22wmf4/includes/Article.php(1472): Article->doDelete('[[Extension:Liq...', false)
#10 /usr/local/apache/common-local/php-1.22wmf4/includes/actions/DeleteAction.php(45): Article->delete()
#11 /usr/local/apache/common-local/php-1.22wmf4/includes/Wiki.php(439): DeleteAction->show()
#12 /usr/local/apache/common-local/php-1.22wmf4/includes/Wiki.php(305): MediaWiki->performAction(Object(Article), Object(Title))
#13 /usr/local/apache/common-local/php-1.22wmf4/includes/Wiki.php(565): MediaWiki->performRequest()
#14 /usr/local/apache/common-local/php-1.22wmf4/includes/Wiki.php(458): MediaWiki->main()
#15 /usr/local/apache/common-local/php-1.22wmf4/index.php(55): MediaWiki->run()
#16 /usr/local/apache/common-local/w/index.php(3): require('/usr/local/apac...')
#17 {main}
Version: unspecified
Severity: major