I also had this problem, and found the following workaround:
1. Load Safari.
2. Go to the preferences screen. (Safari menu -> Safari -> Preferences)
3. Click on the 'Privacy' tab.
4. Set 'Block Cookies' option to 'Never'.
You should now be able to log into the dashboard widget with no issues.
It's worth remembering that this will impact upon your actual browser security settings, however - advertisers will be able to track you using cookies. One possible way around this would be to use a different browser to Safari for your everyday browsing.
I was able to make it work without changing Safari's settings by just logging in to the Toodledo website using Safari and checking the "remember me" box to set the cookie. After that, the widget works fine in the dashboard.