I'm going to answer in terms of the paid labour dimensions of gender. There are other elements of the gendered presentation in Mad Men such as gender and sexual identity, reproduction or unpaid labour.
Feminisation is the change from a male dominated or mixed gender workforce to a female dominated workforce. Proletarianisation is the degradation of: "old" professions; "old" trades; "traditional" labour; or, new work with a high degree of worker control: to management controlled execution of duties as standardised labour (its a bit more complex, but...).
Proletarianisation and feminisation go hand in hand. The women we see working for pay on Mad Men are primarily secretaries. As Margery Davies shows in A Woman's Place is at the typewriter, secretarial duties were once performed by autonomous men with generalised duties. Davies finds in the late 19th century, the combination of employer's views of women as "docile" and "cheap" combined with scientific management, "deskilled" (Harry Braverman) the duties performed, resulting in a rapid feminisation of the workplace.
Likewise, Engels shows that "women as homemaker" is historically contingent, and can change rapidly within a generation as pay changes gendered status, so too does Davies show that secretarial duties' gender position is contingent on the organisation of the workplace.
As far as secretarial duties requiring uneducated labour, IIRC secretarial schools were widespread, and most secretaries were expert business machine operators from tabulators, collators, type writers, telephones, etc.; and the social construction of required duties ranged from trivial to broad ranging. In comparison to equivalent male occupations, skilled machine operation was considered from unskilled through to trade. I would suggest that judged against a male hierarchy of skill, the women portrayed in Mad Men working secretarial work are between unskilled and trade skilled, with one exception of a generalised autonomous worker who occupies a managerial role. Whether we ought to criticise the presence of a unique skill scale for female office work which degraded highly skilled or trade machine operators to "unskilled" work in financial and social respect terms is a political or moral question; but, the presence of different skill hierarchies in farm, industrial or office work, all of which were gendered, ought to raise the question of whether skill hierarchies actually existed or whether they were cover for a gender or industry-based division of labour.
The film depiction has an accuracy as to the broad mentality and sentiment of a white New York set of private capital owners, executives and professionals interacting with a pool of office labour. However, this needs to be read in the context of the Olson and Holloway characters who show this system of work arrangements' flexibility and adaptability in the face of extreme merit and tenacious power; and, so, reading these characters in this way problematises the general gendered order of the office space.
It's no substitute for labour history or gender history, but it is a good starting point for the vibe.