Your description sounds like the way my car felt before I replaced the shocks at 46k. It tended to skitter over bumps around corners. It's definitely feels more "planted" now.I have to preface my answer with the fact that the front struts have 31k miles on them.
The car is a little unbalanced due to the front still having more compression damping than rear. There seems to be a little more willingness for the front to side step some when you corner in a turn with some ripples in the pavement.
The rear seems even more planted now. You can definitely feel the back being more compliant. Hence more grip.
Nothing scary, just different.