Some degree of cassette wobble is normal, especially if it's a screw on freewheel, rather than a cassette.
It probably not related to the chain slipping, but we'd need lots more details to help you beyond that.
SLIPPING? Exactly how? From big sprocket to smaller one, forward when you apply power? Or how and when? The better the description, the better the answer you'll get.
Also, some history, age of the bike, or parts, sudden new problem, got worse over time, or this way as long as you had the bike?
Getting mechanical help via the net is like drawing a word picture. The sharper and more complete the details, the better folks will "see" and recognize what's there.
__________________
FB
Chain-L site
An ounce of diagnosis is worth a pound of cure.
Just because I'm tired of arguing, doesn't mean you're right.
“One accurate measurement is worth a thousand expert opinions” - Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance.
Last edited by FBinNY; 08-29-17 at 08:11 PM.