The 1 x 2 missing-row structure of the Pt(110) surface and its structural 1 x 2 half arrow right over half arrow left 1 x 1 order-disorder transition were investigated using RHEED. Rocking curves were measured at 25 different crystal temperatures between 300 and 1200 K. A dynamical evaluation of these curves, based on a nonlinear optimization scheme, is presented. Furthermore, a new method is used which allows an estimate of the reliability of fit parameters. This represents an efficient alternative to the calculation of R-factor contour plots. It is shown that the rocking curves can be interpreted rather well even in the disordered 1 x 1 phase, if the dynamical scattering is assumed to be from the mean periodic potential of each layer. Structural parameters for the missing-row phase were derived which are compatible with the findings by some other techniques at 300 K: especially a contraction of the top-layer spacing, pairing in the second and buckling in the third layer. We find a 2D-Ising-like decrease of the 1 x 2 order parameter with a critical temperature T(c) = 855 K. About 20-50 K above T(c), an increasing surface roughness can be deduced from different coverages of different surface layers. A decrease of the contraction of the top-layer spacing accompanies the beginning of the roughening.