Hello
I notice that inside the Movable Type admin interface, Action Stream keeps a (permanent?) record of all actions - would it be possible to access this record to make weekly or monthly archive pages of Action Stream activity?
Looking at the sample templates provided with the plugin, I can only see a way to have a single archive page showing activity from a set number of past days, but I haven't used Movable Type since the days of 2.x, so may be missing something obvious.
Any ideas?

That is not currently possible as I understand it. Movable Type has a limitation we hope to resolve in the next release: archives can only be made of entries. Which means MT cannot produce an action stream monthly archive or even an asset monthly archive.
But again, this is a temporary shortcoming. Stay tuned for the release after 4.2... it is likely to have this feature built in.