Yes, I am actually aware of this one. Unfortunately this theme is just becoming a bit outdated and is awaiting a huge update. I’m planning to completely re-do it with my newer framework.
Everything still works with the latest version of WP, but the Twitter is one thing that just doesn’t work anymore. It’s because of the the 3rd party jQuery plugin the theme is using to pull from Twitter. It was originally created back before all the updates to Twitter API happened. You’re just going to have to use some other widget plugin to pull from Twitter for now. I’m sure you can find tons of other free ones. I apologize for the inconvenience.