The same issue affects some of my other gadgets too: most notably, the Flickr, Picasa, TwitPic and Juitter gadgets.
As far as I can tell right now, this issue stems from a sudden, random error affecting any gadgets utilizing User Preferences. These issues do not seem to be affecting every blog in which such gadgets are installed.
The Blogger Team are aware of the issue and are investigating now. I'm also testing various changes to user preferences for my gadgets to see if a different solution to registering user preferences could resolve the issue for my gadgets.
I anyone is still receiving errors when using their Twitter Updates gadget (particularly if this displays tweets from @undefined's stream) please do let me know in the comments or send me an email.