Update – 25.01.2012
I still haven´t found a good solution for the problem. Several people report that they were able to solve it , by changing the owner of the “uploads” directory (to the user which php runs as (in most cases “wwwrun”). But that didn´t worked for me. The only solution I found was to run php as FastCGI and not as an Apache module. This solution though has some drawbacks. You need to configure a single php.ini for every virtual host you run and you can´t use .htaccess files anymore.
My conlusion – FastCGI resolves the problem but doesn´t cure the root of all that evil.
I guess the WordPress 3.3 and 3.3.1 are the worst releases the WordPress Team ever did. First the fucked up the visual editor and now the shittiest WordPress problem ever: “The uploaded file could not be moved to” – a problem occuring when you try to upload images/videos/media (and when your php runs in safe mode).
In older WordPress versions it could be easily solved by chmod 777 the “uploads” folder within “wp-content”. Now this doesn´t work anymore.
One solution is to chmod 777 “wp-content” completely. But they can´t be serious about that…can they ?