This paper examines Einstein’s 1905 derivation of the Lorentz transformations using the average time of travel of a light pulse in opposite directions. It shows that the derivation has significant errors, produces a relationship between the coordinate values that does not exist, and that a more careful examination of his example implies very different characteristics of the velocity of light than those claimed. It also points out that more general derivations which do not address specific measurement conditions cannot be judged as to their applicability. The paper shows that Einstein’s assertion of the independence of the shape of a spherical light pulse from the choice of the inertial reference frame of measurement is inconsistent with the known behavior of the photon. It further notes the impossibility of proving a general set of coordinate transformations, which would require a knowledge of all possible present and future coordinate measurement methods. It gives an example of a photon-emitting clock moving between two photon detectors, for which the transformations of the time of travel of the clock are consistent neither with the Lorentz nor the Galilean transformations.