Hi Denis & Elliot,
I have had exactly the same problem. I have tried fixing it by downloading from WordPress Plugins directly and updating via FTP but noticed that that version is also marked 4.0.2 in the acf.php file.
Thanks
A quick update, it seems the 4.0.3 zip file is missing.
When I look on the developers page here
http://wordpress.org/extend/plugins/advanced-custom-fields/developers/ the SVN repository is there but the zip file gives a 404.
same issue here: Successfully Updated… but then:
“You have version 4.0.2 installed. Update to 4.0.3.”
I was having the same problem so I checked out the svn trunk and got the 4.0.3 update. Works perfectly and does show as 4.0.3 in WordPress. If anyone needs it, i’ve posted a zip of the update to https://dl.dropbox.com/u/22659/advanced-custom-fields_4.0.3.zip
Looks like the auto-update feature beat you to the punch, though… I successfully Updated via the WordPress Updates page just now. “Someone” was listening… 🙂