Another one, less major but still likely worth it is an index on find_new on xf_forum for:
SELECT thread.*,
user.*, IF(user.username IS NULL, thread.username, user.username) AS username,
node.title AS node_title,
forum.*,
forum.last_post_id AS forum_last_post_id,
forum.last_post_date AS forum_last_post_date,
forum.last_post_user_id AS forum_last_post_user_id,
forum.last_post_username AS forum_last_post_username,
forum.last_thread_title AS forum_last_thread_title,
thread.last_post_id,
thread.last_post_date,
thread.last_post_user_id,
thread.last_post_username,
post.message, post.attach_count,
permission.cache_value AS node_permission_cache
FROM xf_thread AS thread
LEFT JOIN xf_user AS user ON
(user.user_id = thread.user_id)
LEFT JOIN xf_node AS node ON
(node.node_id = thread.node_id)
LEFT JOIN xf_forum AS forum ON
(forum.node_id = thread.node_id)
LEFT JOIN xf_post AS post ON
(post.post_id = thread.first_post_id)
LEFT JOIN xf_permission_cache_content AS permission
ON (permission.permission_combination_id = 1
AND permission.content_type = 'node'
AND permission.content_id = thread.node_id)
WHERE (thread.last_post_date > 1386369900) AND (forum.find_new = 1)
ORDER BY thread.last_post_date DESC
LIMIT 60;
