If it was using the British dating system it would be a fraud as 8/7/1961 would be 8th July 1961 which would be before his birth on the 4th of August 1961.
Wiki has a color-coded global map of countries using different date formats and Kenya jumps out all by itself (in purple) as using two formats, one of which matched the Lucas Smith video. It would be possible for Wiki to have been hacked and those with “way-back” investigative skills might want to see how long ago Kenya was shown as using two date formats.
http://en.wikipedia.org/wiki/Date_format#Date_format
List of the world locations by date format in use:
Kenya (d/m/yyyy and m/d/yyyy)
Or...the more obvious answer. The doctors signed the certificate one day, then the next. This often happens with doctors who date it the day they sign it, not the day of the birth. Paperwork is something that often has to be caught up with... I see this as no different, and adds reality to the mix.