I found an issue with the weekly view when the event dates displayed span two years. The layout is incorrect and the events are displayed on the wrong days.
It can bee seen here:
I made it work by setting all the links on the site to use the year parameter with that link:
Without the parameter, the Next and Previous also break (Next linking to 2014 and Previous linking to December 2013). With the parameter they are correct.
The problem is in my-calendar-output.php line 637. Without the yr parameter it sets $c_year to the current year, when it seems it should be set to the year of the first event displayed. The individual event times are calculated later in the code, so a good fix requires more familiarity with the code than I have.
It doesn't seem to affect the monthly view with the same conditions.
The live site above is using version 2.0.6, but I've tested with 2.1.3 and the issue remains. The site is on WP 3.3.1.