The link for the validator is good (in the previous post), and if you do a little searching in your search engine, you can also find multiple test areas (the one in Adobe is great) for checking your site.
The main reason, I believe, that we see problems with Internet Explorer has do to with legacy support. Microsoft has a history of trying to keep their products compatible with their older efforts so that what you produce with their products (and there are quite a few people who use various Microsoft products to publish web content). So, the end result is that as you see the "standard" web products evolve you see compatibility issues that appear as display issues in the browser. To their credit, they have made efforts to minimize these problems and provide solutions (such as the compatibility button in the Address bar), but these problems continue until they decide to remove all legacy compatibility to their own products (for publishing and producting web content) and focusing on only the standards as provided by the W3C.
Remember that they still do have a large share of the market on their platform, and MANY people refuse or cannot afford to upgrade or advance to the next iteration of operating system or browser. You will need to make the decision to determine if your own customer-base will benefit from a website that provides a good experience for the Internet Explorer.