Alan Mattli’s review published on Letterboxd:
Bizarre choices in framing device and narrative structure aside, this is the definition of "fine." Slots in right next to Trumbo and Hitchcock in the canon of visually unremarkable but broadly entertaining stories about the intersection of stardom and politics in 1950s Hollywood, just with less cartoonish acting and zippier dialogue. Kidman and Bardem do good work with the material they're given, even when Sorkin ventures too deeply into his pet quirks (Desi's final speech is such a painful deus ex machina, I was shocked to see it not being revealed as a joke), but the real acting treat here, both comedically and dramatically, are Nina Arianda and J. K. Simmons.
Side notes: there's a nod to the "What a week, huh?" joke from 30 Rock in this; and at one point in this movie set in the early 50s, Lucille uses "gaslight" as a verb, something that, according to Merriam-Webster, was first recorded only in 1956. That latter one is a small and insignificant detail that I normally wouldn't bat an eye at, but here it felt weirdly out of place.