I never heard about VHDs until last week, so I am a fresh baby here. I just received two junk National DP-830s, and trying to do my research to learn how to repair them a bit. I then ran into this forum post through google searches. This isn't my strong suit, considering I only work with game consoles.

One is complete junk, motors are bad, belts are starting to go bad, and couldn't get it to accept a cardtridge, and then 3 of the plastic latching pieces snapped off when I was fiddling with the gears to try and get it to accept the disc (The outside metal of this one looks like it has old mold or something on it so the plastic is probably rotting inside).

The other one, however, takes a disc and plays the one movie that I have, but there is jittering right to left across the entire screen, and the jittering is stronger on the upper half. I'm not sure if this has to do with sending the signal to my 4k tv (its the only thing I have to test it on), the needle, or something to do with the board of the player itself. I wonder if the needle is in good shape to sell, but I have no idea how to diagnose what is creating the screen shake. If I find out the needle is good, and find out the player isn't repairable, it is possible that my friend could put the needle on his store, but that would ultimately be up to him.

Oh good! I have a dp-830 and the loading mechanism grenaded itself in a similar fashion to your model, glad it's common and not just me being far too rough with it or something as for the jitter, I believe it actually has to do with caps because it was getting worse and worse on my DP-330 until it outright refused to read discs. I suppose the real answer here is to recap the video circuit if you can isolate where it is, and see if that makes improvements. And if so, do report your results because the 330 is built very much in the same fashion save for an extra daughter board on the 830

The left-right "shaking" is a result of the unique/unusual time base errors to the VHD format. Unlike LaserDisc, VHD does not have built-in time base correction. Many ADCs (both consumer & professional) can't handle the line to line error and have issues with picture stability. Sometimes, if you gently rock the player back and forth, you can get the image to lock on ADCs that won't cooperate. As someone who recapped multiple VHD decks, recapping will not help this issue at all. It's best to get an 80's to early 90's standard definition CRT TV to test/use your VHD player with; any display of any kind newer or older could have issues with VHD output.
If you eventually lose picture, your needle is worn or dirty and is not related to the above issue. I like gently running the needle over a (moist) Magic Eraser to clean it. If that doesn't help, you need a new needle.

Most National decks suffer from jammed doors from brittle plastic in the front of the loading mechanism (or they quickly break after use). Usually this happens around the spring loaded hinge & snaps for the metal flap. You'll need to super glue the pieces back in place for proper operation.