I haven't got my Wii yet (8th of december) but I've tried it at Churchill Square in Brighton (at the weekend) and its pretty cool... anyhow (enough of the bragging...)
I was under the impression you calibrated the wiimotes? or is that not the case?
if so try recalibrating them...
with the wiimote power problems try changing the batteries... (silly I know - but you can get duff batteries straight out of the box)
is their a range on the Infrared ? (used for the location of the cursor on the screen?)
^ could also be a calibration problem if you calibrate them...
as for the jerky choppy movements... do you have unsteady hands as adrenaline pumps through your body for getting to hold the wiimote :P