What happens if you upgrade one site collection from SharePoint Online 2010 to SharePoint Online 2013, then go to the root site, export it as a template with content, then import the template in a 2013 site collection and try to create a subsite based on that template?
You get this useful error:
An error occurred while processing the request on the server. The status code returned from the server was: 0
Very clean error otherwise:
EDIT: it turns out this is caused by working as a delegated admin. Still a bug, but you can work around this by creating a user in the tenant and giving it site collection administrator rights. Of course, if you have an available license for that.