First off, if that is your website then, you need to hire a new web designer/web developer. Because, CSS/JavaScript and other DOM related errors must be fixed in order to provide better (if not best) user-experience.
Quote:
Is it meant to be like that?
No, and never should be. Why would you want to deliver a web page that contains several warnings and errors.
Most of the errors are for invalid input, some are browser-specific issues. Tell your web developer to support major browsers, and write the code specific for a browser; he can use the HTML comments to enable/disable the CSS files in browsers. There are a lot other ways to solve these issues, but I would leave that in
* the hands of your web developer, to solve them.
* your hands, to hire a new web developer who knows what a warning is, and how to solve it.
Just because your web page renders perfectly on latest Google Chrome or Firefox, doesn't mean it's perfect. Test it across all browsers, and remove the errors... There are many ways to solve a problem, and many problems introduce a lot of solutions, so find one.
Secondly, if this is not your website. Then leave it.