No RSS feed or no feed at all? The situation is simple: no update feed — no update information. The remaining measure would be scanning the whole site, which is in principle can be feasible (Google crawler does, after all) but does not look very practical.
Scanning of the whole site is possible with the number of limitation. The content of some page can be dynamic even when the service part of the code is not updated, so the update is not detectable in principle, also, in principle, the site graph can be
disconnected (
http://en.wikipedia.org/wiki/Connected_space[
^]), so there is no a regular way of discovery of the URLs not
reachable from the head page.
If these considerations do not look too discouraging to you, you can learn and go in for
Web scraping, see:
http://en.wikipedia.org/wiki/Web_scraping[
^].
In my past answers:
How to get the data from another site[
^],
get specific data from web page[
^].
—SA