In addition to what sauoq says, please note that for character classes you need to include square brackets. And your update routine is wrong. Presumably you want something like:

%character_tests = ( 
    var1 => qr/[^0-9]/,
    var2 => qr/[^A-Za-z0-9\.]/ 
);

sub update( $ )
{
   if( $_[1] =~ /$character_tests{ $_[0] )/ ) 
   {
      &set_error_type = "illegal characters";
      return undef;
   }
   else
   {
       $self->{$_[0]} = $_[1];
       return 1; # to match your spec
   }
}
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This will let you assign to var1 only if the value does not contain a digit.