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My book says ethenone is a planar molecule, so I was trying to understand its hybridization,I feel that like allenes ethenone too will not be planar. Supposing oxygen and the carbon near it to be in the xz plane and assuming that the pi bond between them involves py orbital of carbon, this implies the bond between that carbon and the adjacent carbon involves the pz orbital of that carbon. This implies that the end carbon's hydrogens will be in xy plane. What is wrong with my understanding?

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You are right.the hibrydization is the same with allenes but in allenes there are 2 CH2 groups but in ethenone there is a CH2 and there's a O with two none bonding pairs. The hydrogens will be in the same plane as C=C=O but the electron pairs on oxygen are not in the same plane

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    $\begingroup$ But all the atoms are in the same plane. Just to be clear. $\endgroup$ – matt_black Aug 11 '18 at 14:11

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