SME 3012 Help

I just received a SME 3012 Series2 arm, and I am concerned by the looseness of the bearing housing. Specifically, it rocks and twists. I have a SME III which feels much more secure. Is this normal for this arm?
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.)
I used a Denon DL-110 for a long time, and it sounded fine. I've since mounted an Audio Technica 440ML, and it out-tracks the Denon by a large margin. I'll bet the Shure will sound great, that's a classic combination. Best of luck.
The Shure does sound good. The arm is a little heavy to be ideal for the Shure, but in practice it is not much of a problem; the built in damper helps of course.

I prefer the Denon DL103, or at least I did on a SME IIIs(!) with a ballast weight at the headshell and a little lead tape to add mass. I know the Orsonic (or in my case Audioquest) headshell is said to be a good match for the Denon, but in my case it is too heavy. I can't balance the arm without adding lead tape to the counter weight, and the resonance is too low--7hz. As I should have realized with my success using the Denon on the IIIs, it compliance is not nearly as low (in practice) as the stated figure, which in Denon's defence is given at a different frequency than it is commonly expressed, at least in the arm/cartridge compatibility charts. I will try mounting the Denon on the light SME headshell, and if that is too light, I will try something in between like the Sumiko.
I was using the SME headshell with the Denon, and am using a Sumiko with the AT-440ML.