As for why Ross wrote the teleplay, has to do with a cast change which affected the entire plot. As written (according to Lee Meriwether) Lisa Carson was supposed to be the daughter of Mayor Linseed. But when Byron Keith who played the recurring part, wasn't available for the episode, it had to be rewritten. Ross changed the plot to include two new characters. Meriwether became the daughter of millionaire John E Carson, named Lisa (the name of Ross's daughter, King Tut's queen Neila played by Star Trek's Yeoman Rand, Grace Lee Whitney, was named after Ross's wife).
The other new character was Deputy Mayor Zorty (a play on the then Los Angeles Mayor Sam Yorty) played by rotund actor Tol Avery. While the part was small, they needed another large actor to play King Tut at the costume party, While Avery was not in the Buono's league, he served the purpose for the episode.
Lee Meriwether taking a leave from the soon to be cancelled Time Tunnel (also at Fox,) plays the part of Lisa pretty straight. Aside from her dialogue with Tut and her milk and cookies scene at the end of the episode, she is given little to do.
As for the rest of the cast, Lloyd Haynes one of the Fox stock of contract players later to star on Room 222. Haynes died in 1986 at age 52 of cancer. Tim O'Kelly besides appearing as one of the students when the Joker went to school, was the teen sniper in the Boris Karloff film Targets, and disappeared after losing the role of Danny on Hawaii 5-0 to James McArthur (he did the pilot but was replaced). The other two tutlings were Chuck Hicks and Fritz Ford (Hicks is the long time stunt double for Brian Dennehy and Ford was Chuck Conners stunt double on the Riflemen, Barry Dennen later to be the Mexican Bandit with the British accent in Shame's gang next season has a small part as a valet. Dick Bakalyan last seen with the Riddler last season has a small part as an Egyptian pantimime, he will return in larger parts next season.
Terri Messina the young girl who was Dick Grayson's date for the ball was only 21 at the time and died at the age of 60 in 2007. She had small parts on tv shows but her big clam to fame was her long term love affair with Gene Clark of the group the Byrds. She helped him cowrite numerous songs. She spent the last years of her life taking care of her elderly parents.
Columnist Susie Knickerbocker aka Aileen Elder and Aileen Mehle, appeared at the window. She used to be a show biz gossip reporter in the 1960's.
One final interesting note, if you look closely during the bat fight at the boiler works, there are numerous cardboard boxes stacked everywhere, many are labeled stamps while others have question marks on them. Obvious left overs from the Astin Riddler and Colonel Gumm episodes. Nothing at Fox is ever thrown out it is always reused at least one more time.
Next Miss Tallulah Bankhead gives the final role of her career as the Black Widow.