SME 3012 Help

Depends on where it seems loose, and how loose.
The arm tube is on knife-edge bearings, which may seem loose in their normal condition. Or there might be excessive wear or damage. Hard to tell without seeing and feeling the arm.

There is a lot of play as you describe, I just accepted on faith that that was normal for this arm. I've had the arm and the supporting Thorens TD-125 to a turntable clinic, and they didn't find anything awry. It has tracked beautifully as is for 27 years. What turntable were you planning to mount it on?

I have finally mounted it on a homemade birch ply plinth with a Technics SP-10MKII; I should have it up and running tonight. The cartridge will be a Denon DL103 mounted in an Audioquest (Orsonic clone) headshell. I also have a Shure V15VxMR in the SME headshell to try as well. If I don't like the Technics, I will try the arm on a Thorens TD-124, once I get an extended armboard for it. (The Thorens motor needs to be be taken apart and cleaned, I fear. It has noise and speed issues.)