that's a cool looking stout bench lathe! How does the tailstock handle work - is the handle captive and the screw moves through it to move the quill?
Also, it looks like your chuck might not be seating fully against the spindle register (flat part perpendicular to the threads). This will happen if there isn't a recess cut in the chuck back plate for the unthreaded part of the spindle. Pretty easy to fix if so - put a ring on the spindle a bit thicker than the gap, spin the back plate (alone) onto the spindle backwards and cut the recess.