I think I've figured this one out. This is due to another IE bug. The "AppVersion" string that the TD uses to check Internet Explorer's version is too long due to plug-ins and other software installed on your computer. The solution, for now, is to delete some of that extra "noise". You'll have to do this manually. (This does not mean uninstalling any software.)
1) On the Start Menu, select "Run..."
2) Enter "regedit" (without the quotes) in the Run dialog
3) Windows Registry Editor should start. It works a little like Windows Explorer, but you're navigating registry keys instead of your file system
4) Navigate to:
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Internet Settings\5.0\User Agent\Post Platform
5) Right-click on the "Post Platform" key and select "Export". Enter a filename. This will save the registry entries in this key in case, for some reason, you decide to replace them. Think of this as a "backup".
You should now see a number of entries on the right side (now that the "Post Platform" key is selected). I see some entries like ".NET CLR 1.1.4322" and "InfoPath.2", but you could see just about anything. The problem is that if you append each of these together, once they reach a length of 251 characters, the bug kicks in. So you need to delete some of these entries. What you delete is up to you.
It is my opinion that these entries are useless, and deleting them won't affect anything at all. These items build up what is known as the "UserAgent" string. This string is sent to websites that you visit using Internet Explorer. At one time, this was supposed to identify to the website what kind of computer and OS you were running, and other capabilities of your browser. Because this string can be (and often is) faked, very few sites rely on it anymore. Even if it DOES cause problems, you've saved a backup of the keys and can replace them if necessary. But you won't need to.
I would start deleting any entries that appear to be duplicates, with a change only in version number. For example, I actually have 5 entries that look like ".NET CLR 1.1.4322" - all with different version numbers. In a situation like this, I would delete the 4 with the lowest version numbers.
Once you've delete a couple, start the TD again. If you get the error again, continue deleting keys. Then start the TD again. Repeat until the TD starts without error.
This will be fixed (sort of) in version 2.5.6.