Internet Explorer 10 compatibility with SharePoint 2010 (SP 2007 interface)

I am using SharePoint 2010 with the SP 2007 interface. I recently upgraded to IE 10, which appears not to work with several out-of-the-box SharePoint features I've been using:

1. Image Library - When I navigate to an image library, it appears empty and I cannot switch Views.
2. Lookup Columns - When I add a lookup column to a list, the drop-down list in the edit form does not work. I can't see or select any choices other than the default "(none)".
3. People Picker - After I select a user from the People Picker (I'm using forms based authentication) and click OK, I get a Script Error dialog box: "Line: 5    Char: 10990    Error: Unable to get property 'length' of undefined or null reference    Code: 0    URL: https://mydomain.com/ScriptResource.axd?d=QmkNwHMBydRWe6lj6qR5z9aCC8mG...."
4. Rich Text Box - I have a list with a rich text column. In the edit form, the rich text editor doesn't work. It's greyed out as if it's a disabled control.

All of these worked with IE 9 and all work fine in Chrome. It seems like these are all issues with JavaScript support in IE 10. Is IE 10 supposed to work with SharePoint 2010 (with 2007 interface)? Is there any way to work around these issues without asking my users not to use IE 10?

Thanks,

Stephen

Stephen P. Kappel - Sharepoint Developer