The film starts promisingly enough, with some very fun songs and a great plot with tangible stakes. I think the central problem of this film is two-fold though: as Hayworth spends time deciding between fame and her "old life", I don't feel like we get a ton of evidence she's leaning either way.
There are no moments that clarify for the viewer how Hayworth doesn't fit in as a famous person. There's little chemistry between Kelly and Hayworth that really makes clear that they love each other and leaving him is a hard decision. I get that these points are made, but I don't think they are made well. And therefore the payoff at the end just isn't that exciting.
Perhaps worst of all, in the last third of the film, where we should be seeing this conflict play out the most, we get the the three most drawn out musical numbers. Kelly dancing by himself in the window, the Cover Girl performance, and then the back of the army truck ride. Separately they may have been fine, but they all feel so close together and like unnecessary padding.