I just manually copied the 3.5.2 files to my WP 2.7.1 directory, hit wp-admin/upgrade.php and I get this:
Warning: require(/homepages/37/d194393212/htdocs/tanzania/wp-includes/load.php): failed to open stream: No such file or directory in /homepages/37/d194393212/htdocs/tanzania/wp-settings.php on line 21
Fatal error: require(): Failed opening required '/homepages/37/d194393212/htdocs/tanzania/wp-includes/load.php' (include_path='.:/usr/lib/php6') in /homepages/37/d194393212/htdocs/tanzania/wp-settings.php on line 21
Try it for yourself at http://www.bbcafricaslowdown.com
Prior to this I did try the auto-updater (update-core.php) and got a similar mess so I resorted to the manual copy.
Just an FYI -- it may not be related but my provider has turned off PHP4 moving everyone to PHP5. I mention that only because there are some comments in a few of the WP352 files that make a reference to PHP4.
I havbe another site hosted on the same provider (www.coletti.co.uk) which was already at WP3.5x and it is functioning ok.
Any help appreciated.