The Case of the Shapely Shadow

The show opens with a man giving dictation to his secretary. The secretary has styled herself in the manner of the ugly duckling. If she takes off her glasses and loosens her hair, she'll transform into a swan.

The murder centers around corruption in business and the sale of stock.The boss is dictating letters to shareholders.

Boss: And, Janice, no file copy on this as before, and destroy your notes. ... “Gentlemen.” No, change that. Address this one personally to the president of the company, what’s-his-name, and mail it directly to his home.

Janice goes to Perry Mason because her boss has asked her to take a new suitcase to a locker at the bus station. She is worried that the boss is being blackmailed and that she is delivering a payoff. Among other things, Perry asks if her boss is married. Yes, he’s on his second marriage.
PM: Are you afraid if you wore the right lipstick, she might notice you?

PD:: Why is it, every time a beautiful girl walks into this office, my normally intelligent friend --
PM: No, she wasn’t so beautiful, Paul. That’s what intrigued me.
PD: You’re worse off than I thought.

Janice takes off for Las Vegas in some plot twist involving her boss and his first wife (who has seen the error of her ways in letting herself go and now is trying to win her husband back -- even though he has remarried). Perry also goes to Vegas to try to talk some sense into his client. While the women are in town, the boss is murdered at a remote home.

Lt. Tragg shows up with a Vegas policeman.
Snotty officer You’re not on your own bailiwick here, Mr. Mason. This is the State of Nevada. (And later, still sore) Mason, you’re not even admitted to practice law before a traffic court in Nevada.

Speaking of bailiwicks, one has to wonder why the LAPD went to the expense of sending a high-ranking police officer out of state to make an arrest. I'm getting a Lt. Gerard vibe from the whole thing!