How do I validate the "Check for Directory and File Permissions" options in dotProject

You have to change the permissions of the folders suggested by dotProject

  

./ files writable?

     

./ files / temp writable?

     

./ local / in writable?

If you are in linux, you should place the permissions to those folders in 777, or what are read, write and execute permissions.

In linux through chmod seria:

chmod -R 777 /var/www/html/dotproject/files
chmod -R 777 /var/www/html/dotproject/files/temp
chmod -R 777 /var/www/html/dotproject/locales

I do not know dotProject, and Juan Pinzón's answer is valid to some extent, the documentation of dotProject and its source code suggest not to make the "World writable" files, that is, with 777 permissions:

link

<tr>
        <td class="title" colspan="2"><br />Check for Directory and File Permissions</td>
</tr>
<tr>
        <td class="item" colspan="2">If the message 'World Writable' appears after a file/directory, then Permissions for this File have been set to allow all users to write to this file/directory.
        Consider changing this to a more restrictive setting to improve security. You will need to do this manually.</td>
</tr>
<?php
$okMessage='';
if ((file_exists($cfgFile) && !is_writable($cfgFile)) || (!file_exists($cfgFile) && !(is_writable($cfgDir)))) {
    @chmod($cfgFile, $chmod);
    @chmod($cfgDir, $chmod);
    $filemode = @fileperms($cfgFile);
    if ($filemode & 2) {
        $okMessage='<span class="error"> World Writable</span>';
    }
}
?>
<tr>
        <td class="item">./includes/config.php writable?</td>
        <td align="left"><?php echo (is_writable($cfgFile) || is_writable($cfgDir))  ? '<b class="ok">'.$okImg.'</b>'.$okMessage : '<b class="error">'.$failedImg.'</b><span class="warning"> Configuration process can still be continued. Configuration file will be displayed at the end, just copy & paste this and upload.</span>';?></td>
</tr>
<?php
$okMessage="";
if (!is_writable($filesDir)) {
    @chmod($filesDir, $chmod);
}
$filemode = @fileperms($filesDir);
if ($filemode & 2) {
    $okMessage='<span class="error"> World Writable</span>';
}
?>
<tr>
        <td class="item">./files writable?</td>
        <td align="left"><?php echo is_writable($filesDir) ? '<b class="ok">'.$okImg.'</b>'.$okMessage : '<b class="error">'.$failedImg.'</b><span class="warning"> File upload functionality will be disabled</span>';?></td>
</tr>

There is a small discussion about permissions in the dotProject Forum: link

The suggestion is 750 for directories and 640 for files and the user of the web server should be the "owner" of those directories and files (users: apache, www-data, etc ... depending on the case). Assuming that your hosting provider is not very good that we say, you would have no choice but to use 777.