The code that inserts the <div class="aktt_tweets"> code (in function aktt_sidebar_tweets) is guarded by a if (count($tweets) > 0). However, the ending </div> tag is added regardless of how many tweets there are.
The result is that if you have no tweets, you get an extra </div> tag that can wreak havoc with your sidebar.
Guarding the </div> tag with a similar if statement solves the problem.