Is there any reason to keep http://todoist.com/m#overview
I have run http://todoist.com/m#overview simultaneously with my usual todoist on the webpage because I wanted access to my to do lists off line. Given your update, is there any reason to run http://todoist.com/m#overview anymore?
the todoist.com/m page is mainly optimized for touch-controlled devices such as mobile phones and tablets. Now that Todoist is fully HTML5 compatible with offline storage, you may indeed use the full web-app only and once you disconnect from the internet, you'll be able to continue working on your tasks.
Furthermore, if you access it through this URL: https://todoist.com/app?v=53 it will be available even if you're already offline.