My daughter has been travelling since she was 1 year old, and we never had any problems until earlier this year. My daughter is a dual citizen (US/Costa Rica), and in Costa Rica they wouldn't let her leave (with her mother) without a government endorsement in her passport.
This is a bit spotty, however, the next time we went (after I had spent 1 1/2 days standing in line at the CR government offices), they didn't even look at it.
However, it ruined a great vacation in Argentina for my wife and daughter. (I was in Argentina already, from the US).