Actually, Codger, the star is only mentioned in connection with the magi and may not have been an "obvious" thing except to them (assuming they were astrologers of some sort). Might not even have been a "star" as such (maybe a conjunction?), that might just be a sort of shorthand used by non-astrologers to describe what drew the magi.

One does wonder why Herod didn't insist on some sort of "honour guard" for the magi, just to make sure he did get the info he wanted.