You should pursue all of the previously mentioned advise items. I have a Pioneer PL-530 and am the original owner. Bought it new in the 70's. There are numerous issues that can arise with tables of this vintage, such as speed variations, tonearm return point, strobe performance, etc. I'm not sure how similar your 510 is to my 530 but there are probably many common components that each share.
One advise thing I didn't see mentioned is possible cracking of the plastic tonearm base (if the 510 is of this construction). This is very common with Pioneer tables of this vintage.
First test is to grasp the tonearm between the head shell and pivot and push and pull toward and away from the pivot. Gently. Use no great force. Notice if you feel any play at all no matter how slight. If you do then inspect the tonearm base. There are a lot of Google results on how to fix this problem. Even if you do not detect any play in the arm I would still not rule out that problem.
Best of luck.
One advise thing I didn't see mentioned is possible cracking of the plastic tonearm base (if the 510 is of this construction). This is very common with Pioneer tables of this vintage.
First test is to grasp the tonearm between the head shell and pivot and push and pull toward and away from the pivot. Gently. Use no great force. Notice if you feel any play at all no matter how slight. If you do then inspect the tonearm base. There are a lot of Google results on how to fix this problem. Even if you do not detect any play in the arm I would still not rule out that problem.
Best of luck.