I don't know if anyone has suggested this already, but put centers in both headstock and tailstock. Retract the quill and bring the tailstock up, lock everthing and check for alignment. Now backoff the tailstock and extend the quill and check for alignment again. That will tell you if there is a problem with the tailstock. Measure any errors, and note if they are vertical or horizontal.
If the tailstock seems ok, the only way I can think of to test the rotating headstock is this. Rough out a cylinder, maybe 2x6, between centers. Now put the cylinder in the chuck, true it up and make a nice face on the end. Mark the center of the end face with the tip of a skew chisel, and bring up the tailstock center and check for alignment. Do this with both the quill in and out. Now carefully part off the cylinder, face it off, mark the center and test for alignment.