Applying categories to multiple nodes

Since I converted my existing site to Drupal I've found the taxonomy to be superb, generally speaking - users can freely tag their content and new stories, blogs, and forum topics always have multiple categorisations. The only annoyance I have is that often once these new categories are created, it's obvious that they should be applied to piles of previous pre-Drupal content, and there's no easy way to do this.

For instance, say someone writes an article about Star Trek and posts it with under a "Star Trek" tag - there might be another fifty stories or forum topics about "Star Trek" already in the database, but they're all under old categories such as "Television" or "Sci-fi". For me to apply the new tag to those old articles, so they're all listed under Star Trek (as well as their original categories), I have to manually search, locate, and edit each and every node to add the "Star Trek" tag, which is a long and laborious process.

What would be great would be some way (or perhaps some module) in which I could search for "Star Trek", come up with a complete list of all the matching nodes, and then apply the new tag to all of them all at once, with one click. Is that possible?

Even better would be something clever enough to do that automatically... but I guess I'm drifting into fantasy there?