Hey poppy,
MS when it 'first' presents, doesn't typically produce sx's on both sides of the body, it usually hits one side first but over time and with newly developed lesions, its quite likely to then experience MS sx's on both sides.
What MS doesn't typically do is produce symmetrical sx's, so same sx's in the exact same place on both sides of the body at the same time, eg both feet or both hands etc. MS doesn't produce 'all over' or rapidly spreading sx's, or new sx's every other day.
When it comes to spinal lesions, the sx's are more predictable eg bladder/bowel, sexual dysfunction etc but just like brain lesions, there are different diseases that cause them, size, shape, horizontal vs vertical etc. MS spinal lesions do produce sx's below but in order for 1 lesion to effect both sides 'equally' the lesion would need to be very large or laying vertically and from my lay persons understanding, that wouldn't be very common in MS.
We have a health page that explains spinal lesions and its well worth reading
http://www.medhelp.org/health_pages/Multiple-Sclerosis/Spinal-Cord-Lesions/show/764?cid=36
Cheers........JJ