This letter investigates the use of spectrally efficient pulse shapes in a physical layer network coding (PNC) system. A multi-user detector is used in the form of a maximum likelihood sequence estimator that accounts for offsets in timing, amplitude and phase between the two incoming signals in the multiple-access phase of a PNC system. It is found that with root-raised cosine (RRC) pulses, the PNC system is much more sensitive to timing offset in terms of the performance of the receiver relative to when rectangular pulses are used. Simulation results confirm that it is necessary to keep the incoming signals aligned to within about 1/10th of a symbol interval to avoid substantial performance loss.