The hole in Guatemala City is not a sinkhole. When you inspect it, it doesn't even look like one. The sides are clean and featureless, and the shape is crisp and geometrical. It helps to know that Guatemala City is in volcanic country, not limestone country. In fact the city, like many in Central America, sits in a former river valley that is filled to the brim with loose volcanic tuff. When something compacts it at a deep level, or when groundwater flow carries it away, the tuff can settle downward. Reilly interviewed a geologist practicing in Guatemala who gave us the correct name for this structure and its formative process: a piping structure. Piping is also called tunnel erosion, and it's always a concern around large dams, for instance, or when a water main or sewer line breaks underground. It's also a concern in other Central American cities like San Salvador, where the tierra blanca tuff is prone to compaction. Take a look at the pictures from the Guatemalan government's Flickr site, and see the feature with new eyes.
Photo courtesy Govt. of Guatemala, Creative Commons license