Eftersom MySQL inte stöder fönsterfunktioner, tror jag inte att det finns något sätt att göra detta utan en underfråga:
SELECT f.id AS forum_id,
f.name AS forum_name,
t.id AS thread_id,
t.topic AS thread_topic,
t.ts AS thread_timestamp,
p.id AS post_id,
p.content AS post_content,
p.ts AS post_timestamp
FROM forums f
JOIN (SELECT t2.forum_id, max(p2.ts) as ts
FROM posts p2
JOIN threads t2 ON p2.thread_id = t2.id
GROUP BY t2.forum_id) max_p ON f.id = max_p.forum_id
JOIN posts p ON max_p.ts = p.ts
JOIN threads t ON f.id = t.forum_id AND p.thread_id = t.id
ORDER BY p.ts
Naturligtvis skulle cachelagring av de senaste resultaten låta dig göra detta utan prestationsstraffet att anropa MAX(), men med rätt index borde detta inte vara något problem...
UPPDATERA
Det mest kortfattade sättet att inkludera trådar utan inlägg och forum utan trådar skulle vara att använda LEFT JOINs istället för INNER JOINs:
SELECT f.id AS forum_id,
f.name AS forum_name,
t.id AS thread_id,
t.topic AS thread_topic,
t.ts AS thread_timestamp,
p.id AS post_id,
p.content AS post_content,
p.ts AS post_timestamp
FROM forums f
LEFT JOIN (SELECT t2.forum_id, max(COALESCE(p2.ts, t2.ts)) as ts, COUNT(p2.ts) as post_count
FROM threads t2
LEFT JOIN posts p2 ON p2.thread_id = t2.id
GROUP BY t2.forum_id) max_p ON f.id = max_p.forum_id
LEFT JOIN posts p ON max_p.ts = p.ts
LEFT JOIN threads t ON f.id = t.forum_id AND (max_p.post_count = 0 OR p.thread_id = t.id)
ORDER BY p.ts