The 'Add to Google Calendar' link that appears on single events pages is generating links that are way too long, resulting in a 414 error from Google.
As far as I can make out this is down to interaction with other plugins, specifically for me with JetPack's sharing plugin. TEC checks the length of the event description and takes action to ensure it is not too long if necessary. But it then applies 'the_content' filter. At some point, and I guess this is the point, the sharing plugin adds around 3,500 characters to the description, taking, in my case, a 452 character description which passed the length check to a 3,960 character description which causes Google to throw a 414 error.