I agree with the comments that the film was made to be light, and an escape from the everyday worries of the time period. I actually find it a little frivolous. One would presume, based on the title of the film, it is meant to pay tribute to Ziegfeld, but just in the clip, it feels a little superficial,and comedic. I would think that the actual rivalry between Ziegfeld and Billings would not have been as good-natured as was portrayed here. Afterall, this was also business!
Anna seems very easily distracted, and a little child-like, not only with the song selected, but also in the way she keeps going back to the flowers, and how pretty they are. She doesn't seem to need a lot of convincing to meet Mr. Ziegfeld Jr.
I think the idea of the woman being a rival for men's attention and affection, is a continuous theme, not only in depression era films, but one that continues today. I think another, would be how money is used, as a source of buying favours. Example, the doorman, and the bouquet, of "all the orchids in the world".
As for the change due to the code - I think Anna's costume may have been different, before the code. Her dress was quite demure - for a "French" singer. I think that would have played more towards a "Moulin Rouge" style of costume, prior to the change. More of a stereotypical version of a French showgirl.
American values are clearly visible, in the paintings of the former Presidents on the walls, the flags, and the American ships around the office. The dialogue revolves completely around patriotism, from the butler talking about seeing Cohan in George Washington Jr., singing about the proud, old flag, to Cohan referring to Yankee Doodle Dandy, and FDR speaking about how the Irish Americans carried their love of the country proudly. I don't think the film would have been as effective, starting with the parade, because of the importance of the dialogue by FDR. He talks about the patriotism of the Irish Americans, which allows Cohan to "flashback" to the parade sequence. Eventually it will all tie together, but it's shows how Cohans ideals, and his own patriotism, was initially nurtured and developed by his parents.