MARGO: Don't get stuck on some glamour puss. […] you're a setup for some gorgeous wide-eyed young babe.
Bill's eight years younger than Margo. This conversation between them is our first indication of Margo's insecurity about her age. She's constantly afraid Bill will leave her for someone younger. Someone like Eve. To his credit, Bill's completely indifferent to their age difference.
MARGO: You bought the new girdles a size smaller. I can feel it.
BIRDIE: Something maybe grew a size bigger.
MARGO: When we get home you're going to get into one of those girdles and act for two and half hours.
BIRDIE: I couldn't get into the girdle in two an' a half hours...
It's not just romance that Margo's insecure about. With age, she has to work harder to maintain her figure. It's not just vanity. It's critical for a woman in her profession to look slim and glamorous.
MARGO: Don't let me kill the point. Or isn't it a story for grownups?
Margo lashes out at Eve. Here she uses her age to her own advantage, insulting Eve for being too young. She's also trying to make sure that Bill knows Eve is too young for him.
BILL: I've always denied the legend that you were in Our American Cousin the night Lincoln was shot...
This is one of many jokes about Margo's age. Bill references it to both tease her for her sensitivity about her age, and to show that he defends her from her critics. He's not worried about her age because he knows how he feels about her. Margo's the one always on the defensive about it.
MARGO: A milkshake?
Eve is offered a drink and Margo suggests a milkshake. Margo may be angry for always being described as "too old," but she has no problem trying to insult Eve's youth. Is this hypocritical behavior on Margo's part?
MARGO: "Cora." She's still a girl of twenty?
LLOYD: Twentyish. It isn't important. […] Margo, you haven't got any age.
MARGO: Miss Channing is ageless. Spoken like a press agent.
Margo has no illusions about what it means in the theater to be her age. The longer she attempts to play younger parts, the more likely she is to be considered delusional vs. ageless. Another Oscar-nominated film released in 1950 was Sunset Boulevard, in which an aging silent film star is clearly considered delusional for wanting to get back in the spotlight.
MARGO: (reading Addison's column) […] "Miss Harrington had much to tell, and these columns shall report her faithfully, about the lamentable practice in our Theater of permitting, shall we say…mature actresses to continue playing roles requiring a youth and vigor of which they retain but a dim memory."
"Professional mud-slinger" Addison has no problem brutally criticizing Margo in his column. He's perpetuating ageist beliefs in an attempt to benefit Eve by taking down Margo.