With this simple process I worked on this week, I can now create an animation of mapping progress in OpenStreetMap within 2 hours or less, it depends from how many files it needs to process for GIF.
For that a have made a tutorial where explain step by step how to make a GIF animation of progress tracing in OSM, maybe is not unique way to do that, but it is a good way using Tilemill how doing that.
Progress from all tracing and import buildings in New York between 10/01/2013 and 04/08/2014
Progress from all tracing in San Francisco between 01/09/2013 and 04/09/2014
Progress from all tracing buildings by Team Tracing in San Francisco between 01/09/2013 and 04/09/2014