The CDM9 swingarm & laser mech is very robust, if it works at all, it is likely good. The laser movement is driven by voicecoil type actuator - so no traverse wormdrive mech to stick/slip/need the rails cleaning; and the laser position and focus positioning is servo-controlled by a Phillips IC, so none of the old-style focus/gain/offset pots to adjust.
Also, while it is apart, wipe-down the tiny turntable to check it's not the cd just slipping.
The later CDM12.1 uses a linear drive sled (again, servo-controlled - nothing to adjust) - in which case the prime suspect for incidental mistracking/glitching is to wipe the sled, rails and worm drive clean with alcohol on a q-tip and try it again.
The temptation is to re-grease but IME over many years of dicking with cdm/vam12+ mechs they last longer/stick less with no lube (the sled worm & gearing is nylon, so lube has to be silicone and very sparingly applied if at all - not any old grease, esp not oil-based)*
From the OP's symptoms, if the disc is loading properly, but mistracking randomly and in an irritating manner - I'd guess this is a CDM12.x based player. And I'd definitely try to fix the orig mech in terms of cleaning sliding parts scrupulously before trying a current 'new production' vam1201j replacement or sim - they are mostly cheap, and bad, copies and you may need 4-5 to get a good working one :/
*ETA: It's an old story, but a large batch of CDM12.1 mechs delivered by Philips to Micromega with the wrong grease applied is essentially the thing that killed the first incarnation of that company - the mechs all 'stuck', and as a small op they didn't have the capacity or margin to repair/replace all and maintain production, while allegedly Philips shrugged it off. Of course I read this secondhand...