When I update drupal core or even a couple of modules, I'm always afraid if something breaks. What easy way is there to test a site if anything has broken? Its not feasible for me to test a site that has over 1000 pages.
In general Drupal core updates should not break Drupal core. If you upgrade
stable community modules to a newer
stable release -- again you should not encounter regression error problems.
That being said and long as your not the edge with alot of modules it shouldnt be such a huge worry -- but I similar worries. Backup, Backup, Backup always.
I doubt you have 1000s of unique pages. There are tools like Selinium, or JMeter or Java's The Grinder that let you script interactions with a webpage for known results. You could script your set of possible necessary functionalities on a handful of generic pages.
There's no way around testing if you really have to test and assure error-free site usage.
I use Selenium, which has nothing to do with Drupal but is open source. I use the Selenium IDE Firefox extension on my machine locally, but Sauce Labs also offers paid services (I'm not a customer but I've heard good things).
Basically, with these tools, you define a series of tasks step-by-step. Then, when you update core/modules, you run the tests and make sure they return the correct results (you define what the correct results are).
This takes significant time to set up. When I was first starting out, it took me about three days to get a decent set of tests. However, now I can quickly check for all the past known problems whenever I update my site, so I think the investment was worth it.