How can I fix my ID3 tags without confusing iTunes? I'm planning to use TagScanner to clean up the ID3 tags for my music (though I'd be happy to use an alternative if it addressed the problem below). Unfortunately, doing so will change the files out from under iTunes. One thing that worries me is that iTunes seems to like to keep my music in folders reflecting the artist's name. 
Once TagScanner has fixed the tags some files will be in a folder that's inconsistent with what one would expect based on the tags. I'd also like to make sure that iTunes' view of of the music reflects the updated information so that, for example, I can search for files using the repaired ID3 tags.
How can I spruce up my music files without breaking iTunes?
One idea would be to run TagScanner, then create a new iTunes library: 


Hold Option while starting iTunes.
Click "Create new" library. Choose its destination ~/Music and name it.
In the new library, open Preferences and navigate to Advanced.
Make sure that "Copy files to iTunes Media folder when adding to library" is checked.
Import all the TagScanner'd music files into your new library. 


iTunes will create a new folder/sub-folder [artist/album] hierarchy based on the new ID3 information, and nothing would be broken. If everything looks the way you want it to, delete the old library. Here's how to delete the old library (this edit is in response to your comment below): delete the entire /iTunes folder and all its contents. You'll notice that when you make a new library, you get a new folder in ~/Music. For example, ~/Music/Nathans_Library. That folder isn't where the iTunes application lives, so it's fine to wipe out the whole thing. 

(It's handy to know this, because it means you can store your iTunes library wherever you want to. For example, at work I archive loads of audio tracks in an iTunes library on a server. That way, my co-workers can access it if they need to, and our ITS department can back it up more easily.)

One tip for albums featuring guest appearances: Set the album artist, because iTunes looks at "Taylor Swift" and "Taylor Swift feat. Tim McGraw" as two separate artists, so make sure to set the album artist to "Taylor Swift". iTunes will use the album artist field to make the organizational folder hierarchy, so your tracks will stay grouped together in the file system as well as in iTunes.

Caveat: Following this approach might mean losing your personal metadata like play count, rating, date last played, etc. I'm not sure though. 

Definitely back up your entire iTunes library before trying anything like this; you never know what might cause you to need a "do-over".