I had to manually tweak my DNS service providers BIND file.

BIND file, created by professional hosting company, before:

$ORIGIN mycoolsite.com.  
$TTL 300  
@ SOA ns1.cheapreg.com. registry.cheapreg.com. ( ... )  
@ IN 3600 NS ns1.cheapreg.com.  
@ IN 3600 NS ns2.cheapreg.com.  
@ IN 3600 A 199.9.99.85  
@ IN 3600 A 199.9.99.86  
* IN 3600 A 199.9.99.85  
* IN 3600 A 199.9.99.86  
www IN 3600 A 199.9.99.85    
www IN 3600 A 199.9.99.86  

BIND file, created by layman, after:

$ORIGIN mycoolsite.com.  
$TTL 300
@ SOA ns1.cheapreg.com. registry.cheapreg.com. ( ... )  
@ IN 3600 NS ns1.cheapreg.com.  
@ IN 3600 NS ns2.cheapreg.com.  
* IN 3600 A 219.94.116.50  
* IN 3600 A 219.94.116.51  
* IN 3600 A 219.94.116.52    

The difference is that the "pro"-file has duplicated the nameserver entries, once for @, and once for *,
and I haven't.

Any reason I should also duplicate nameserver entries (@ and *) ?