I was having a problem running the Twitter List Widget on my Microsoft Internet Explorer 8 also. The widget would appear but no information inside would stream. It would work fine in FireFox or other browsers, just not in IE. The problem I found was with Twitter widget.js file that was being called from the source they provided for me to paste on my site.
The actual .js file that is on the Twitter server has an error in it that won't allow the IE browser to display the stream. I was able to fix this rather simply. I downloaded the .js file by pasting the path in my browser:
Once I had the .js file, I opened it using notepad to view the source. The change that needs to be made is simple, use the "Find" command in notepad to look for the word "array" and when it finds the entry, make the following change:
Change the entry that says “Array.forEach” in the widget.js file to read “Array.prototype.forEach”
By adding the word "prototype" you have now corrected their mistake. Of course you can't upload the file to their server so just place it in a directory on your site and path to it directly by changing the path in your Twitter generated source to point to the .js files new location on your website.
I hope this helps! Have a great day!