The Slow Wonder was met with generally positive reviews, with a Metacritic rating of 80 out of 100 based on 21 reviews. Brandon Stosuy of Pitchfork said the album "fits together for a taut 34 minutes without lags or rough spots" and could be "viewed as collection of singles." Tim Sendra of AllMusic wrote that standout tracks such as new wave sound of Secretarial combined with the sunny power pop of "Miracle Drug" or "On the Table" makes "[The Slow Wonder] essential". In another positive review, Rolling Stone said "Newman pens melodies that seem to have sprung from the collective unconscious and then encases them in bright, lush power-pop arrangements."
There were a handful of less than positive views on the album. Alternative Press said the album "sounded like demos" Newman was preparing for a future release. Although Anthony Miccio of The Village Voice wrote "uptempo grins like "On the Table" make denying the pleasantness of it all impossible," he proceeded in criticizing it for just being "pop," and being "just something to zone out to."