Luke mentions "the Scarecrow incident" a reference to the villain of the same name. Coincidentally, in Batwoman's first appearance in Elseworlds, Part 2 (2018) Oliver and Barry are subjected to Scarecrow's fear toxin.
The first four episodes of the season took place several months before the Elseworlds crossover, and the next four episodes before the Crisis. This episode brings the series up to the present day, taking place after the Crisis, yet everyone is acting like Alice's murder of Catherine just happened recently. Although given that several Cosmic Retcons happened during the Crisis, this is possibly justified.
In the comics, the Batcave is often shown having a large animatronic T. Rex, a big Joker playing card, and a giant penny, supposedly souvenirs/ trophies from some of Batman's adventures. The computer in the Batcave that Luke uses on the show has a plastic T. Rex on it.
Slam Bradley was depicted as a private eye who can "slam-bang his way out of a barroom brawl or mob attack", and often liked working cases brought to him by other women, but enjoyed the "platonic company" of his sidekick, Shorty Morgan. While the character was largely well-received at the time, "Slam Bradley" stories have come under scrutiny for racist caricatures of antagonists. The character came to life after Malcolm Wheeler-Nicholson conceived the idea for the character in a letter to Jerry Siegel, and was created by the two men alongside Joe Shuster. Slam Bradley made his official debut in Detective Comics #1, a year before Superman and two years before Batman, and became a fixture in the series until Issue #152. Slam then disappeared from DC canon for over 30 years, but re-emerged in Detective Comics #500 and in various Superman titles (which also established his successor, Slam Bradley Jr.). He then made his most prominent return in the "Trail of the Catwoman" arc, in which he investigated the death of Selina Kyle and went on to become a fixture in the ongoing Catwoman series.
Kate and Luke compare Slam Bradley, the cop who first rescues Kate and later gets rescued by her, to Captain America, even more specifically the Chris Evans version. Kate also mentions Mr. Robot.