Respectfully, I think you have to stretch this film pretty far to get it anywhere near "Blow-Up" or "La dolce vita", thematically speaking. "Medium Cool" simply surveyed the atmosphere of America in the late '60s, while simultaneously being critical of the corrupted media, oppressive authority, and passive atmosphere of the hippie movement, all of which the film depicts as being counterproductive to a healthy society. "Blow-Up" is not actually a political film at all, not beneath the surface, anyways. It's much more philosophical than it is political. "Blow-Up" is about the unreliability of perception, the inherently subjective nature of existence itself. It examines the mod London scene on a topical level, only as a means of peeling off that superficial layer and examining the reality (or, in this film, the unreality) that lies beneath. As Antonioni says in "Beyond the Clouds", via his alter-ego (played by Malkovich), examining what lies beneath the surface layers of the society and the reality that surrounds us has been the single objective of his entire career as a filmmaker. "Blow-Up" isn't actually interested in the culture of '60s England at all, the way "Medium Cool" is in the American culture of the late '60s. It's interested in much deeper, existential problems that transcend both time and place. London just happens to be the setting (because Antonioni had signed a deal with MGM to make three English-language films), but it could have just as easily been set almost anywhere else, and the same themes would dominate the film. We can't say that of "Medium Cool". As for "La dolce vita", that was a much more personal film than either of the other two, about the search for "the sweet life" and the ultimate realization that it is nowhere to be found. Of course, there is some criticism of the media in Fellini's film, but like Antonioni's film, "La dolce vita" only engages society and culture insofar as it needs to in order to explore its other, more dominant themes. Fellini shows the absurdity of '60s Italian society in order to convey the milieu responsible for the personal alienation of the individual (like Antonioni's concurrent Italian films). But Fellini's film is, at heart, about that personal alienation it is about the individual, not about the society or the culture itself, which, as in Kafka, is only a backdrop of absurdity against which the existential struggle of the individual can play out. Whereas "Medium Cool" is about the society, the culture and the individual is merely a focal point to give viewers something to center themselves around while they absorb Wexler's attempts to both capture and criticize the realities of late 1960s America.

The film also bears some similarities to La Dolce Vita (1959)

Well, they're both '60s breakthrough films, anyway.
Play the game existence 'til the endof the beginning

Yes! I felt the presence of Blow Up particularly in the final shots - the shaded greenery of the final drive and the passing car taking a snap of the couple in the flaming station wagon. Death in a well-groomed park as an ironic statement about detachment.
"And a Happy New Year to you, George Bailey. in jail!"

A bit of a stretch. Blowup is a mystery(plot)something Medium Cool surely isn't. Medium Cool seems similiar to LaDolceVita which deals with a journalist and his photographer as Medium Cool deals with a cameraman and sound man. The film LaDolceVita inspred the word paparazzi. Medium Cool also seems influenced by Godard whose films used poster art, documentary realism, and distancing devices.

Also, Breathless (1960) and many others. Wexler is first and foremost a Cinematographer. It's only natural that he'd subliminally reference his favorite things in his directing debut.

For some reason, I kept thinking of "The Man With A Movie Camera" while I was watching this.