If you look closely at Moth's costume, it would later be redressed and used as Batgirl's costume in the final season.
Except for the episode of Ring of Wax in which an unnamed Mayor appears, Gotham City is presided over by Mayor Linseed. Linseed's name was s spoof on the name of then New York City Mayor John Lindsay. Never seen, but at times referred to was Governor Stonefellow, a play on the name of then New York Governor Nelson Rockefeller. In addition, the episode King Tut's Coup featured a Deputy Mayor Zorty, whose name was taken from then Los Angeles Mayor Sam Yorty.
If you look under the front bumper of the Batmobile, you will see the Bat Ram folded underneath. It won't be utilized until the following episode, "Give 'em the Axe", and is not utilized or visible in any episodes for the remainder of the series.
The Riddler spends most of this two-parter engaged in carrying out a complicated plan to steal "the fabled Lost Treasure of the Incas", which he believes is hidden in the sarcophagus of a Peruvian mummy. Actually, although it certainly wouldn't have fit into a sarcophagus, there really IS a legend about a Lost Treasure of the Incas: it was said to have been a "lifesized" garden molded entirely from pure, soft gold - including a huge, gold-covered disk representing the Sun - which decorated the courtyard of the Incas' Temple of the Sun. If this treasure ever really existed - or continues to exist, in some hidden corner of the world - no trace of it has ever been found.
The Batmobile exits the Batcave and goes around the danger sign (which is there, but not facing the camera). Then we see The Batmobile pass the Gotham City sign in a view not normally seen (from the rear) and enters highway to the right. This scene is on the 2014 DVD release.