Answered: How to bulk delete/reject questions awaiting moderation?

I don't think the Web UI provides a simple way of doing this, but you can easily remove those posts directly from the database. All posts under moderation have a type ending with the suffix "_QUEUED," so you can use that as the filter for a DELETE query.

DELETE FROM qa_posts WHERE type LIKE "%_QUEUED";

If you want only a particular type of post removed (e.g. only questions), change the filter to that type (e.g. type="Q_QUEUED").

Note that removing posts under moderation directly from the database will not automatically reset the counter for those posts, so you'll have to do that yourself as well.

UPDATE qa_options SET content=0 WHERE title="cache_queuedcount";