I had a sleep study and it showed that I had mild (10 episodes per
hour) sleep apnea but my desaturation level went down into the mid
thirties.  I really don't have COPD that could cause this.  At the
time I had the sleep study, my potassium level was quite low.  Could
this have caused these low saturation levels?  Should I take this
study over?

What do the people who ordered and did the study tell you? That's the
best source of answers for your particular situation. The desaturation
you describe is quite significant. Ask your doctor what she thinks
about it. The causes for sleep apnea are several, as are the
solutions. It sounds like you have reason to look into it further,
with your doctors. And no, low potassium would not explain such a
level of desaturation.

I am not quite believing that your "saturation" went down into the
"thirties" for any significant period of time.  That value is not
compatible with sustainable life.  You stated that you do not have
COPD.  Therefore I would guess that your normal Sp02 (Saturation of
the partial pressure of dissolved oxygen in your blood) is usually in
the normal range of 85 to 100.

Here is a graphical representation of the oxyhemoglobin dissociation
curve.
http://www.biotech.um.edu.mt/home_pages/chris/Respiration/oxygen4.htm

When I perform sleep studies, I always generate a hard copy of the
monitored values on continuous graph paper...the kind that is little
red lines (not like school drafting graph paper).  All the monitored
values will be indicated in a continuous scribe, corresponding to
numbers indicated in the paper margin.  Some typical monitored values
are: respiration pattern, heart rate, maybe gastric pH (if a patient
is being monitored for gastric reflux), and of course, Sp02.  The
professional person who evaluated your sleep study can see if there is
"artifact" such as a probe which may have fallen off, and therefore
indicated a low value, very easily.  If your Sp02 really did go to
"30's", then it stands to reason that your respiration rate and
pattern, and possibly your heart rate, would also change. 
SIGNIFICANTLY.

I agree with surgeon-ga, go back to the interpreter of the test and
ask for clarification.  You can ask to see the graph output.

10 episodes of apnea per hour likely results in a diminished quality
of sleep and likely also interferes with your "awake" quality of life.
 Are you exhausted despite seemingly adequate "hours spent in bed"? 
Are you cranky and irritable without explanantion?

Did the physician recommend a CPAP unit?  (Continuous positive airway
pressure) Go back to the doctor and ask more questions.