Kolchak explains that a mace is a spiky ball on the end of a chain. Technically, that 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". The writer, likely, did this as a way of showing that the pompous Rausch isn't as smart as he thinks he is.
The Police Captain's last name, "Rausch", is the German word for being drunk or high on drugs.
Thete is paper in the baskets behind the teletype machines at the end credits. Usually, the baskets are empty.
In a departure from his usual voice-over narration, Kolchak only provides the day of the week and the time. He doesn't provide the usual month and date like he does in the other episodes.