Spurious signals around LO feedthrough in HP 8591A spectrum analyzer?
I would recommend checking the first LO, in particular the YIG voltages on a scope. Any excessive noise on those supply/tuning lines could translate to side bands around the LO.

Similar checks for the 2nd LO will also be useful.

edit: the REF unlock error looks suspicious, and would point to some unwanted modulation of the LO.