After calculating backward isentropic trajectories on the PC and looking at the plot, particularly the vertical motion plot at the bottom, I see motion across theta surfaces. My question is, shouldn’t I see vertical motion on a constant theta (potential temperature) surface?

The model is quasi-isentropic. That is, the trajectory is not forced to stay on the isentropic surface, but the vertical motion component required to maintain a parcel on the surface is computed for each grid point based upon the slope of the surface and the horizontal velocity component. The trajectories departure from the isentropic surface is a measure of how good the isentropic assumption is for that case. Normally the trajectories do not cross surfaces, but they may under strong diabatic conditions, i.e. in the boundary layer or through regions of latent heat release. This may be reflected as jumps in the trajectory as the trajectory uses data from the next analysis fields, which may not always be consistent with the fields at the previous time.