If you look on our demo website at the javascript of the checkout page, you can see that code:
var hikashop=Array();
hikashop['reqFieldsComp']=Array();
hikashop['validFieldsComp']=Array();
hikashop['reqFieldsComp']['register'] = Array('name','username','email','password','password2');
hikashop['validFieldsComp']['register'] = Array('Please enter a value for the field Name','Please enter a value for the field Username','Please enter a value for the field E-mail','Please enter a value for the field Password','Please enter a value for the field password2');
hikashop['reqFieldsComp']['address'] = Array('address_title','address_firstname','address_lastname','address_street','address_city','address_telephone');
hikashop['validFieldsComp']['address'] = Array('Please enter a value for the field Title','Please enter a value for the field First name','Please enter a value for the field Last name','Please enter a value for the field Street','Please enter a value for the field City','Please enter a value for the field Telephone');
That code specifies which field is required. Since your fields are of the table order, you should add something like that:
hikashop = Array('my_custom_field_column');
hikashop = Array('Please enter a value for the field My field');
Or then remove these arrays when needed via some javascript.