I just did a fresh install of 3.6.1 and unziped the file directly on the server.
It says: "Total files changed: 209/961" . You appear to have a large number of files not matching their original checksums.
Either you've got a LOT of files customised, the wrong checksum file is being used, or you are using a patched (incremental) update.
All .php files and mostly from /modules and /includes.
What is wrong here?