Is there a way to force iTunes 11 to update tags?

From the MusicBrainz iTunes Guide:

Updating Library in iTunes

Brute force method (full library re-scan)

This method works best if
- you've re-tagged a whole lot of your files and don't remember which files/albums
- or there are far too many for the first approach
- or you've moved/renamed files and iTunes has lost them

Ready?

• Go to File > Add Folder to Library
• Point it at the top of your iTunes directory ("My Music\iTunes\iTunes Music\Music" on Windows, by default).
• iTunes will rescan your music, but recognize it's already imported, so you shouldn't end up with duplicate files (unless you have moved/renamed files)

You can also refresh a selection of songs by following the AppleScript based solution (on the same page linked above):

Mac-only advanced method

This method is a bit more complicated to set up, but easy to use.

Fire up Script Editor (which is under Applications/AppleScript, but it will work with TextEdit). Paste the following code, then save as a Script called /Library/iTunes/Scripts/Refresh.scpt (create the Scripts directory if it doesn't already exist).

tell application "iTunes"
refresh selection
end tell

Now, inside iTunes, you should see a Scripts menu (an icon of a scroll, just left of Help). The "Refresh" item on that menu will force it to re-read the tags for all tracks that you have selected.

You can go to iTunes->Preferences->Advanced, uncheck Keep iTunes Media folder organized, OK, then go back and check the option again. It will rescan all track after you click OK.

Building on M K's answer, the following script won't stop the first time it hits a file which can't be found:

tell application "Music"
  repeat with aTrack in selection
    try
        refresh aTrack
    end try
  end repeat
end tell

Edit: in MacOS older than Catalina, change "Music" to "iTunes" for this to work.