One thing for certain is that it is not the best browser for Magento eCommerce stores.

Your customers will be starting to use Internet Explorer 9 so you should check the new browser is compatible with the Frontend of your Magento eCommerce store by testing it thoroughly with all the features in your store, login, product add, remove, checkout etc.

There are already reports of problems with the older versions of the Javascript prototype library not working correctly in the Frontend. And there are multiple problems when you try to use IE9 in the Admin backend of Magento 1.3.x.

Until Magento releases an official update for IE9 issues, a possible workaround that may resolve rendering problems for your site is to use the X-UA compatibility META Tag to try and force Internet Explorer 9 to use IE8 like handling of content.

If you experience compatibility problems try turning on compatibility mode in IE9 by clicking the small compatibility button in the “one bar” (address bar). If this resolves the problem you can implement the compatibility META tag by editing the head.phtml file of your themes template e.g. app/design/frontend/YOUR THEMEt/default/template/page/html/head.phtml in older Magento versions.

The following Meta TAG should be placed directly below the <title> tag

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<meta http-equiv="X-UA-Compatible" content="IE=8" />
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Save the file, refresh your site and test again. If you don’t have access to edit your sites template files Alan Storm has created an IE9 extension patch that will insert the tag automagically for you.

For the backend I would just recommend not using IE if possible at least until Magento releases a patch.