Hello,

what version of Joomla! are you using? I am surprised this does not work because the module does not create the links, it uses the Joomla! API to create them.
Are you using an external extension/tool (for SEO/SEF handling) ?

You are actually observing a normal behavior for the article part of the paths created (for instance '...noticias/noticias-programa-de-ecoturismo/657-nuevas-tarifas-de-ingreso-a-los-sectores-turisticos-del-acg'). Menu items of categories and single articles that are not called from menu items show different behaviors. Actually, paths would be short if every single article had a menu item associated to it (and therefore use the alias).
In your page www.acguanacaste.ac.cr/biodiversidadacg/...nes-de-biodiversidad, for instance, one article path created by Joomla! is www.acguanacaste.ac.cr/biodiversidadacg/...x-mitratus1406167262.
It has the long article path (594- ...)because no menu item is associated to it.
Try the regular latest news article module coming with Joomla! and see what kind of links you are getting. You should see the same behavior.

Now, that does not take away the fact that you should not get '/component/content/category/' in the paths. We need to find out why it happens (it obviously is abnormal).

By the way, you have an error, the category 'Noticias de Educación Biológica' has no menu item associated to it. So calling it will definitely give you a 404.

To get it out of the way:
you have articles with category alias:, not.

So, with the 'Latest News' module, you confirmed the problem comes from the framework, not the module itself.

Now, we have to find out what it is. It may be linked to the way you have the international site setup.

Could you send me credentials for your administrator console at [email protected]? I will take a look tomorrow. It's midnight here and I am beat. Thanks!