HTML error after file upload in WP 3.5.2

After upgrading to WP 3.5.2 I now encounter an HTML Error after uploading any size file (even small ones) to my site. I’ve tried adjusting PHP limits and .htaccess:

<IfModule mod_security.c>
<Files async-upload.php>
SecFilterEngine Off
SecFilterScanPOST Off
</Files>
</IfModule>

None of these was of any help.
Are there any ideas on how can I enable file uploads again?
It did work in previous WP 5.3.1
Thanks.