How common is it for a patient to suffer a serious complication from a
spinal tap, such as paralysis?  Is the risk of complications dependent
to some extent on the doctor's level of experience?  The cites I've
looked at talk about risks but they do not give any indication as to
how frequently complications occur.

These two reports may be of use:

The chance of post-lumbar puncture headache is from 15 to 30 percent.
Factors involved in determining likelihood of such a headache include
or may include the reasons for the lumbar puncture, the age and sex of
the patient, and the size of the needle.
http://healthsciences.columbia.edu/news/review/archives/medrev_v1n2_0003.html

Cerebral herniation can occur after a spinal tap, but it is not clear
whether this is caused by the tap, is made more likely by the 
tap, or is as a result of the natural progression of the disease that
led to having the tap done.
http://www.med.monash.edu.au/healthservices/cce/evidence/pdf/c/961.pdf

Hi -

If I find the time, I'll try and find the sites and formalize this as
an answer - the most common complication of spinal taps (the medical
term is lumbar puncture) are headache (given as below as 15-30%),
leakage of cerebrospinal fluid (CSF) (around 1-2%, depends on the size
of the needle), serious bleeding (around 1%) and infection and
subsequent epidural abscess (around 1-5% - greater in
immunocompromised patients).  Paralysis is a rare complication of
lumbar puncture as the site of puncture is below the spinal cord
proper and into the sac that surround the cord - at lumbar levels, the
spinal cord terminates around L2 and spinal taps are done around L3-L5
thus minimizing the chance of spinal cord direct trauma).  Spinal taps
can cause very nasty side effects if the patient has an intracranial
mass that is affecting the flow of CSF - in this case, decompressing
the spinal cord can lower the pressure in the spine and shove the
brain down into the spinal canal with bad results - if an intracranial
mass is suspected, a brain CT needs to be done before a spinal tap.

synarchy