Well, so I've been doing some more tests, and I've narrowed the source of the error to the permalink settings.
It seems that the error triggers if the generated archive URLs and the permalink structure-based post URLs partially overlap; this is what I've found:
* Permalink structure is mysite.com/%postname%/ (one of the options provided by WordPress)
In this case, the error doesn't trigger and everything works fine, since the generated archive URL is mysite.com/2014/06, while the URL of a given post is mysite.com/thepost
* Permalink structure is mysite.com/%year%/%monthnum%/%postname%/
In this case, the error does trigger; I believe this is because the generated archive URL is still mysite.com/2014/06, while the URL of the posts is now mysite.com/2014/06/thepost. There's overlap, and the language switcher error takes place as described in my first post. (this was my permalink sctructure when I noticed the error)
This is confirmed with another test:
* Permalink structure is mysite.com/%year%/word/%monthnum%/%postname%/
With this, the error doesn't trigger, because while the generated archive URL is still mysite.com/2014/06, the URL of the posts is now mysite.com/2014/word/06/thepost. No direct overlap, no error.
Sadly, the following is not a solution:
* Permalink structure is mysite.com/blog/%year%/%monthnum%/%postname%/
Adding a prefix or suffix to the structure doesn't fix anything, since these are also parsed into the archive URL, again causing the error.
Knowing all this, there's probably several ways of creating a workaround, but I thought you would probably be interested in correcting this behavior in future versions of the plugin.