Your ballhead is probably the one-knob kind. You need the 2 knob kind - 1 to release the ball, 1 to pan.
If you're not very critical, what I usually do is to just handhold and twist my body to take pictures, without moving my feet. Make sure that there's plenty of overlap and make sure you're using the same exposure for it. That's where M mode comes in handy. I use a free, pretty simple software called The Panorama Factory by Smoky City Design. Mine is v2.4 but there probably are newer versions of it online now. Otherwise, I think Photoshop can also do stitching.
K, probably way too much info there. You just asking about the ballhead right? =P
Haha! Not cannot make it la. It will have its uses. Anyway, most of my panorama shots are taken handheld rather than using my tripod, even though my ballhead has a panning knob. Because u need to ensure that the ballhead is confirm very horizontal, then the panning will be useful. Otherwise, I can stand on slanted ground and still take panoramas handheld.
And you're right about the vertical movement. I try to use a continuous line as a guide lor... plus, there are gridlines in my viewfinder to help with that.
With parallax errors, there is no way you can stitch a proper 360 pano without some overlapping errors and the pano will appear improper however, a pan head will allow depending on scene and what stitching application you use to stitch to stitch at least a row of images to form a flat pano.