How to replace an empty date value?
For starters, your GUI shouldn't matter, but it's normally good to use the CLI - i.e. the mysql client - or at least as a backup in case of results you are having problems interpreting.
Second, have you tried IS NULL instead of the = comparison? 
Third, what's wrong with NULL? Normally, you should use the appropriate datatype - why is NULL a problem? If you don't know the date of birth, there's nothing wrong with it. For example, if you want to perform an AVG calculation, you'll have problems. Your population will appear much older than it really is. NULLs however will be ignored in such a calculation, so no anomalous results (the same goes for all such calculations).