Knowledge about the current and future states of a radio channel takes the reliability of a communications system to a new level. A Radio Environment Map (REM) contains information about the channel state in the spatial domain for a given environment. Given a known user trajectory, this information can be used for channel prediction. In this work, we investigated the two primary limitations to this approach: the required spatio-temporal stationarity of the channel and the high localization accuracy of the user. The channel stationarity is quantified by repeated channel measurements. The high measurable consistency indicates the value of REMs in non-changing environments. Based on a high-resolution REM that we measured in an office environment, we quantify the impact of one- and two-dimensional localization errors on the resulting prediction error. With the results shown, localization accuracy requirements can be derived given the target channel prediction accuracy. Also, the results help to determine the required spatial resolution of REM measurements in practice.