Tim, I mean no offense but your post is difficult to understand because of your terminology. It might be a good idea to use conventional nomenclature so we all understand what we're discussing. Movements along the longitudinal axis of the lathe is called the Z-axis. Movements across the lathe from the front to the back is called the X-axis. So, when we
turn a work piece we do so in the
longitudinal or Z-axis, and when we
feed in or face, we do so in the
X-direction with the cross slide or compound. I assume that when you say "longitudinal" you mean a turning cut and a "lateral" cut is a facing cut or you are feeding in a depth of cut. If this is not correct, please let us know.
Issue 1. Over time, I noted replicability issues; there was/is a bit of slop in both longitudinal (what I call east-west) and lateral cutting. I measured carefully each time, but could not pin down the ability to replicate a cut.
Can you clarify this for us? Do you mean that you could not accurately dial in a specific depth of cut and expect the lathe to take that off the diameter?
Issue 2. The compound was just too difficult to adjust. I disassembled it, discovered that both swivel bolts were bent, clearly the cause of my inability to get the swivel to work well. This appeared to have been a traumatic injury, as if something fell on the compound or the compound was used to move the lathe; everything else around it was sound.) I replaced those through the actuator. [Issue 3.] When I got it all back together, it would no longer hold a cut, either turning or facing. It bucks off the work for a cut of more than 5-8 thou, and with the less resistance the tool just pushed away from the work. I noted that the cross-slide, when pushed, moved appr 1/32", you could jiggle it back and forth. Tightening down the gibs did not eliminate this (the 820 has no cross-slide lock, a project for the coming weeks with a friend with a drill press). I could not tell if the loss of lateral rigidity (what I call north-south) has the same cause of the inability to hold a depth of cut.
Not sure what the "actuator" is but you replaced the swivel pins (I assume you mean the swivel pins, part # 180, that lock the compound down to the cross slide) and subsequently noted that there was excessive movement in the cross slide or the compound (do you know which one is moving?), such that a depth of cut more than 0.005 - 0.008" pushed the tool away from the work.
Issue 4. Based on the comments here, lateral slippage was excessive. Based on advice here, the next step appeared to be disassembling the cross-slide more completely. I removed the QCTP and compound again, removed the cross-slide thread nut, and this time opened up the handwheel and collar assembly. It showed that the threads between handwheel and inside jam nut were damaged, perhaps from the same traumatic injury that bent the compound swivel bolts (one can imagine someone grabbing the lathe by the cross-slide handle and compound). With advice from here, I located a 3/8-24 UNF die nut, repaired the threads, removed the nut. As noted above, I was not able during this attempt to dislodge the woodruff key, so could not get the cross-slide screw out, but cleaned out a lot of old crap and reassembled. (Robert, thanks for the download reference; I have that doc here and can now see the woodruff key.) The cross-slide slippage appeared to be much improved, showing almost no free turning of the handwheel.
So, it appears that fixing the damaged thread on the part of the leadscrew that takes up slack between the cross slide leadscrew and nut allowed you to reduce the amount of play in that assembly but ...
I tightened down the gibs, and it held tight, no lateral movement. I stuck a test piece of steel into the chuck; it turned without slippage, but after releasing the gibs a quarter-turn and, with the first facing attempt it bucked, and now the lateral slippage is back again. In fact, it's worse; the entire cross-slide now jiggles both longitudinally and laterally. The carriage and saddle assemblies are firm and rigid. All of the motion is above, with the cross-slide. When I tightened down the cross-slide gibs again, it holds firm. Are the gibs that sensitive?
Which gibs did you tighten - the cross slide or compound? Assuming you mean the cross slide gibs, your issues resolved until you loosened the gibs a quarter turn and the issue of "lateral slippage" recurred.
So, from what I can gather here, it appears that
the problem is that the cross slide gib is extra-sensitive, such that you have to run it tight to eliminate turning and facing issues. Is this correct? If so, it implies that the gib or the dovetail is not flat or is not adjusted correctly. I am not clear on how replacing the swivel pins that hold the compound to the cross slide affects this other than that they now work properly and are transferring forces from the tool to the wonky gib situation.
Do you agree with the problem statement? If so, then the guys can maybe help you work through the evaluation and resolution of this problem. As we discussed, it might not be a bad idea to use some Prussian Blue to see what the contact pattern looks like under there. You might also take a really close look at the gib adjustment screws to see if there is any deformation at their tips. With luck, this might all be resolved by replacing the gib.