The accuracy of the observed time difference of arrival (OTDOA) in the long-term evolution (LTE) systems depends on the accuracy of the time of arrival (TOA) measurements, which are often corrupted by various errors caused by non-light-of-sight propagation, multipath interference, noise, and path detection techniques. Furthermore, signal bandwidth, channel condition, distance from the evolved node-B, and scatterer distribution are the affecting parameters on the OTDOA accuracy. Since the user equipment obtains the most accurate TOA from the resolved first arrival path (R-FAP), understanding errors of the TOA and OTDOA from the R-FAP is necessary to develop OTDOA positioning techniques. In this paper, we develop theoretical expressions for the TOA and OTDOA error distributions of the R-FAP for outdoor multipath environments by integrating theoretical models of the errors expressed with the affecting parameters, and theoretical expressions are verified with numerous Monte Carlo simulations. In addition, we propose an LTE OTDOA positioning technique that compensates the mean TOA offset in the TDOA measurements before applying a positioning algorithm, and we demonstrate the performance improvement using Monte Carlo simulations. In this paper, we do not include OTDOA errors due to the network synchronization and intercell interference.