It is shown that a determination of critical exponents in surface phase transformations based on a kinematic analysis of LEED peak intensities is subject to errors caused by multiple scattering that are large enough to prevent a clear assignment to a known universality class. The multiple-scattering contribution arises from short-range flucutations and has its maximum value at the transition temperature. The specific-heat exponent of the surface phase can be measured directly from the variation of the integral-order-beam intensity with temperature that is caused by the multiple scattering.