The main thing that I did was take off the main arm (please forgive my amateur terminology) and took off the stylus. There was an automatic Start/Stop feature that I also had to repair.
I took the stylus off of the arm. This is one thing that may have been a mistake. The stylus can be rotated and mounted at different positions along two channels. What should I be looking for when I find the correct mounting position/angle?
I guess I should have started out stating my problem. Everything works great except every once in a while the record will skip. The sound is great. I hooked it up through a preamp and fixed the wiring and cables. The records seem pristine, however still will skip. This will happen after a few minutes of playing at different locations on the record.
Currently the counterweight is adjusted all the way towards the stylus; the stylus has a lot of pressure. What should I look for when it comes to adjusting the counterweight?
There is another knob near the pivot of the arm. There are numbers 1-3 with many hash marks. What does this do and what should I look for when adjusting it?
The anti-skating feature, as I see from the mechanical 'guts' of the player, adjust the rebound tension of the arm. Is this just a trial-and-error setting? I understand that there are different settings for spherical and elliptical styli. What is the difference? The stylus is a Shure M95ED.
There are also screws on the top and side of the pivot of the arm. Is there any reason to worry about these?
The arm would not go all the way to the 'last groove' point (again, forgive my terminology,) once a record is complete.
All of these problems lead me to believe that there is too much tension pulling the arm to the outside causing it to skip. If I put a small amount of pressure near the pivot to push the needle inside it plays seamlessly. I guess I am posting my own troubleshooting procedure but with only questions on how to set it up.
I understand that this is a loaded question but bear with me, I purchased my first records today and, not only don't want to ruin any records, but want to continue the purist musical listening experience
Thank you in advance for any advice
ADDITION:
When the needle gets toward the center of the record, the problem occurs much more frequently.

