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After calculating backward isobaric trajectories I see that the pressure is not constant and looking at the vertical motion plot at the bottom of the plot, I see vertical motion (about 500m difference from the starting point to some other points ). Why is this?

The isobaric (and other options) are not truly "iso --" but quasi because the motion is only approximated by computing the velocity required to maintain the parcel on the iso surface. When the next time period's meteorological data are read in, a parcel may find itself on another surface. So the departure from "iso" is one measure of the precision of that particular trajectory (precision not accuracy, that is another issue). As to the vertical motion plot, you must be careful because the vertical scale is height above model ground level, not pressure level. So that as you are traveling along a pressure surface the distance between the ground and the trajectory endpoint will change (decrease with higher elevation and increase with lower elevation).

I hope that answers your questions.

Glenn Rolph and Roland Draxler NOAA ARL