Well, that warning tells you the permissions are not okay. Are you on a shared server? In case PHP is handled in DSO mode (Apache module), you need to make virtually every directory and file in your Magento installation world writable in order to use Magento Connect. This is because the web server needs to be able to write to your files. This is potentially a big security risk as also other users on the server will be able to overwrite/delete your files.
If you still want to use Magento Connect, you should change the permissions on every directory in your install (including the Magento root directory) to 777. Files should be 666 to be writable. At least, then the error message should go away.
Again, I do not recommend such permission settings on a production store. If you have SSH access, you can use PEAR to upgrade or install extensions.
If PHP scripts are executed under the script owner (e.g. suEXEC/suPHP), permissions of 755 for directories and 644 for files should work.