Why is my used Ultegra 10-sp cassette wobbly to the touch on a new Ambrosio hub? All spacers present/correct and 11-sprocket well-seated before torquing 40nM lockring. I tried another (used) 10-sp 11-21 cassette on the same hub and there is no wobble for that one. Puzzled!
Note: Different cassettes may need different spacers.
Unless there is a defect in the cassette or freewheel, it should not wobble (at all!) when properly installed.
Try removing and cleaning the cassette (a bit of dirt can cause it to get skewed a bit). When you put the cassette back on, make sure there is about 1 mm of cassette sticking past the freewheel hub before putting on the locking ring. If the cassette is not sticking past, then (just like a compression headset), you won't be able to tighten it properly and you will need to put additional spacers behind the cassette. Tightening a lock ring without the correct spacing can also easily strip the lock ring (which is better than stripping the threads in the freewheel, but will still ruin your afternoon).
If there is still ANY wobble, a visit to your LBS may be in order.
There's a bearing that rachets between the cassette and the axle. If you are in a very low gear and crank hard up a hill, that bearing can get warped or crushed. (I did it, that's how I know). Bike mechanic can replace it ... they have the tools.