Today, Péter helped me pinpoint an error affecting all Last Comments gadgets in Internet Explorer. If you are using a custom or third-party template for your blog, sometimes the font information does not get passed correctly to gadgets. In Péter's case, only the font name was being sent to the gadget, and Internet Explorer does not allow the "style.font" attribute to be set to just a font name--the font size must also be included. This was causing Last Comments to freeze up in the loading process in Internet Explorer browsers on blogs that are using custom or third-party templates. A fix has been rolled out and this problem should no longer be affecting the gadget.
Also, I fixed Last Comments 1.3 for Private Blogs so that the "number of comments" setting is observed correctly. Some tips for people using Last Comments 1.3, if you get stuck in an endless cycle of logging in and loading and the gadget doesn't seem to work, try closing your browser and restarting it. That should clear the errors because the authentication cookies are only stored until the browser is closed.
If you do not want to close the browser, try looking through your cookies in your browser for a cookie with an extra long domain made of random letters and numbers followed by the words "opensocial.googleusercontent". It will have a cookie name of "g314-scope-0". Delete that cookie and go through the login process again.
The other option is to log in to your Google account and remove all of your AuthSub tokens here: https://www.google.com/accounts/IssuedAuthSubTokens. There is a limit to how many you can have at one time, and if the gadget is taking you through and endless cycle of logging in and loading, then you might have exceeded that limit and need to clear the tokens you have been issued by clicking on "Revoke Access".