Having listened to ["Playing Possum"] more than half a dozen times now, what clear and precise thoughts does it provoke? The answer is, to the best of my ability, that there's little provocation at all, beyond, that is, the picture on the cover….
The songs within comprise music of controlled sensuality, but the mood is too languorous to generate much real heat. Carly Simon's a tease and a society broad. You knew it with "You're So Vain," but on "Playing Possum" she extends that role, even to the point of including a song called "Are You Ticklish."… It's tempting to think of her as Joni Mitchell without depth; even her sensuality seems mere artfulness, the refined and coolly calculated product of the debs' finishing school. Although the title cut is really a reference to the present attitude of sixties activists, it can be interpreted as expressing the emotional low-profile of the whole album….
[It] must be worrying for Ms. Simon's commercial aspirations that there aren't any really memorable tunes or hook-lines here, although the single that's been released, "Attitude Dancing," enjoys a pleasant rhythmic propulsion in the chorus. Certainly there's nothing as obviously infectious as "You're So Vain."…
It should be said … that she does have moments as a writer. Anyone who can write, in "After the Storm"—"the wind's pulling the moon down, underneath the eiderdown," has some talent going for them; lyrically, in fact, it's a finely-felt song about screwing, probably the best on the album. Her problem, here at any rate, is an inability to translate that vital impulse into music with the same emotional impact.
Michael Watts, "Carly: Sensual Promise, but No Hot Cakes: 'Playing Possum'," in Melody Maker (© IPC Business Press Ltd.), June 14, 1975, p. 36.