As Dan says, the smearing does suggest too much wax may have been used. You only need the thinnest layer of any kind of wax, be it hard, paste or liquid. Finish kare is paste wax and although liquid and paste waxes are generally easier to apply, it also makes it easier to put too much on. Much harder to put too much of a hard wax on, because, well because it's harder!
If you ever apply a paste or liquid wax using a DA, you'll see just how thin and even a layer goes on via the finishing pad. It's a great lesson in exactly how little wax is needed and is then very easy to buff off by hand with a MF. Not possible to apply hard wax with a DA.
After you next wash the car, go round and give it a really good buffing to try and shift any still on. If you are still having issues after that, I would remove the wax which you can strip off with a very concentrated shampoo wash and start again, being very sparing with it next time round. Good luck and let us know how you get on.