Kolchak explains that a mace is a spiky ball on the end of a chain. Technically that is what is known as a flair or a "morning star". A mace has the striking portion (blunt or edged) attached directly to the haft.
Capt. Rausch misquotes Shakespeare when he repeats the famous line from Hamlet, "There are more things in heaven and earth, Horatio, / Than are dreamt of in your philosophy." Rausch incorrectly says "under the sun". This was likely done deliberately by the writer, as a way showing the pompous Rausch isn't as smart as he thinks he is.
It isn't clear why the Police Captain was given the last name of "Rausch", but it's the German word for being drunk or high on drugs.
When attempting to describe a mace to a morgue attendant, Kolchak invokes the films of Errol Flynn and Robert Taylor. Although Darren McGavin worked with neither actor, a decade later when a TV movie was made based on Flynn's autobiography, My Wicked, Wicked Ways: The Legend of Errol Flynn (1985), McGavin portrayed Dr. Gerrit Koets, a longtime friend of Flynn who had assisted in his writing of the book, while Flynn was portrayed in the film by Duncan Regehr. Simon Oakland, by the way, had worked with Taylor in an episode of the latter's fifties drama series The Detectives (1959).
If you closely at the baskets behind the teletype machines at the end credits you can see paper in one. Usually you don't see any visible paper.