I tried upgrading a local 3.1.9 and 3.1.10 to 3.2.0 using "Update filesystem and database" and "Download modified files in an archive". I downloaded the archive with the new files, replaced them and clicked "Check files again". The result: these two files keep getting listed under "Not modified files":

• assets/fonts/fontawesome-webfont.ttf
• ext/phpbb/viglink/styles/all/theme/images/VigLink_logo.png

I click on "Update files". Then I'm offered to download the archive where these two files are in, "Check files again" or "Continue update process". When I click "Check files again" I stay in the update loop with these two files, but "Continue update process" still works and everything is done.

So the updater keeps telling me there are two files I need to update (otherwise I wouldn't be offered to download them, right?) even though they are already there and the update can continue regardless.

One more thing: when I updated from 3.2.0-RC2 to 3.2.0 and used the same update process as above, after the first file replacement there are no files listed that still need updating, so the above problem only occurs when updating from 3.1.x it seems.
However, the "Download modified files archive" is still displayed even though there are no files left to update/download. When I click on the download button I get "Information The file specified could not be found."

These two issues don't prevent me from completing the update process, they merely cause minor confusion.