Errors can occur when saving some of the sample charts if your server has the Apache mod_security module configured, with protection against SQL injection attacks. A common mod_security rule returns a 403 (access denied) error if a request includes a SQL "UNION" statement, because UNION can potentially be used as part of a SQL injection attack. See this page for more details:
http://stackoverflow.com/questions/19448257/403-forbidden-if-the-word-union-is-found-in-url
The error is normally a 403 but we have also seen cases where a 404 error was generated.
To confirm whether this is the problem you are facing, try saving a chart that does not include a SQL UNION statement. If that works, then the problem is probably the UNION mod_security rule. In most real charts, you won't need to use UNION, but if you do, you will need to ask your web host to remove that mod_security rule for your account.
Other mod_security rules can generate errors when saving charts, even without UNION statements. A good way to confirm the problem is to blank out the SQL query and click the Close button. This will not save the chart, but does still transmit all the form data back to the server, so mod_security can still generate an error. If the error goes away without the SQL, the problem is almost certainly caused by a mod_security rule.
Some cPanels allow you to switch mod_security on and off, even if they don't give you access to the rule configuration.