re-wiring tonearm

I'm re-wiring my vestigial tone-arm and have noticed that the original wiring had both left and right ground wires connected and grounded to the metal body of the arm. Surely this is wrong? Don't both grounds have to go separately to the right and left channels? And don't both have to be shielded from the metal of the tone arm? Also, the RCA connectors and cable are the dollar-store variety. Will I get better sound if I use an expensive RCA cable and connectors?
Your tonearm is wired correctly. Grounds are common and are tied in together. If you look at any component you will see that the ground wires are all connected together. Since you are rewiring the arm you might as well upgrade the cable and connectors.