mennofied - I think it highly depends on the cart. This issue has been discussed & apparently carts have tipped over but I know the carts around here are a couple of different designs & I just make sure that it seems stable to me. There are some carts I won't put the bucket on but few stores have that style anymore (kind of a deep basket with a small child seat at the front). Some people will say that absolutely never to put a bucket on top but I think that is a little over the top.
fwiw - now that's it's warm I don't bother with the bucket anymore & just babywear - I just find it easier, but I seem to have babies who are not content to sit in the bucket.