Not only is Cinco de Mayo not Mexican Independece Day, but it isn’t even celebrated in most of Mexico.
This NPR piece explains it well: http://www.npr.org/blogs/codeswitch/2014/05/02/308624630/cinco-de-mayo-whose-holiday-is-it-anyway?utm_source=facebook.com&utm_medium=social&utm_campaign=npr&utm_term=nprnews&utm_content=20140502
On a less serious note, here’s a list of Cinco de Mayo Do’s and Don’ts from Buzzfeed: http://www.buzzfeed.com/adriancarrasquillo/20-dos-and-donts-of-cinco-de-mayo
Bruce Critchley's Mexico Here and There 