But-2-yne and hydrogen (one mole each) are separately treated with...

But-2-yne ($CH_3-C\equiv C-CH_3$) undergoes partial hydrogenation.
Reaction with $Pd/C$ (Lindlar-like conditions for 1 mole $H_2$) gives cis-but-2-ene as product $X$.
Reaction with $Na/liq. NH_3$ (Birch reduction) gives trans-but-2-ene as product $Y$.
Statement A: $X$ (cis)$and Y$ (trans) are geometrical isomers, hence stereoisomers. This is correct.
Statement B: Cis-but-2-ene ($X$) has a non-zero dipole moment ($\mu \neq 0$) due to the additive nature of bond moments, while trans-but-2-ene ($Y$) has zero dipole moment ($\mu = 0$) due to symmetry. Thus, statement B is incorrect.
Statement C: Cis-isomers generally have higher boiling points than trans-isomers due to higher dipole-dipole interactions. So, B.P. of $X > Y$. This is correct.
Statement D: Reductive ozonolysis ($O_3/Zn, H_2O$) of both cis-but-2-ene and trans-but-2-ene yields the same product, ethanal ($CH_3CHO$). Thus, statement D is incorrect.
The incorrect statements are B and D.