Well, to begin, this error usually only shows up in Internet Explorer and it mainly has to do with JavaScript. If the Web site you're trying to view uses JavaScript, you may run into a script related error, which triggers the "Done, but with errors on page" message. It is usually generated by an error in the site's code and unless you have access to that code, you probably won't be able to fix the error yourself. Once the problem hits a Web site's code, only the developers of the site can get in and fix it. It looks like this, by the way:
In addition, if you're a Web site designer or editor yourself, you'll want to keep an eye on your site and make sure the "Done, but with errors on page" message doesn't pop up at any time. If it does, just go in and look through your source code. The problem usually comes from an improper syntax, an incomplete code or a script that is placed in the wrong HTML section. Just take a look at those things and you should be able to fix the error rather quickly. Then your site will be back up and running the way it should be.
As you can see, this error message isn't one to panic about. It's unfortunate that it happens, but there's not really anything you can do about it yourself. If there's any way you can contact the designer of the Web site, do so. They may not even know there's a problem, but if you tell them, I'm sure they'll get it fixed right away. Otherwise, you'll just have to sit tight and keep checking back until the problem is solved. Luckily, it's not an error message that can ruin your whole day. At least it shouldn't!