Explain why Gauss' Law doesn't work on dipoles.

The electric field multiplied by the area of the surface projected in a plane perpendicular to the field is what we call electric flux, Gauss's Law is an important tool since that allows the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. Gauss's Law is a general law applying to any closed surface with sufficient symmetry. Considering that to find electric field is convenient when charge distribution is symmetrical in some way, dipoles encloses no net charge, so the flux through it should be zero due to their asymmetry.

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