Why are bicycle pedal threads' handedness left on the left and right on the right? I understand the reason that bicycle pedals are oppositely threaded on either side. What I don't understand is why it works because I'm missing something.
Take the right pedal for example. It's threads are right-handed, so it would be tightened by turning it clockwise (if the pedal were in between you and the bike). Now imagining this from the same perspective, a person pedaling makes the right pedal constantly turn counter-clockwise, relative to the crank. If there's any friction between the pedal and the bolt attaching it to the crank, I would imagine that it would create a force that would try to turn the bolt counter-clockwise along with the pedal.
This is the opposite of what happens, and I've seen the bolts unthread after pedaling backwards a lot myself. What am I missing?
 A: I don't know if it's right or not, but Wikipedia has this to say:

The right-side (usually the
  drive-side) pedal spindle is
  right-hand threaded, and the left-side
  (usually the non-drive-side) pedal
  spindle is left-hand (reverse)
  threaded to help prevent it from
  becoming loose by an effect called
  precession.
Although the left pedal turns
  clockwise on its bearing relative to
  the crank (and so would seem to
  tighten a right-hand thread), the
  force from the rider's foot presses
  the spindle against the crank thread
  at a point which rolls around
  clockwise with respect to the crank,
  thus slowly pulling the outside of the
  pedal spindle anticlockwise
  (counterclockwise) because of friction
  and thus would loosen a right-hand
  thread.

A: Take the right pedal as an example.  It uses a right-hand thread, so turning the pedal spindle clockwise (CW) relative to the crank will screw the spindle in, counter-clockwise (CCW) will unscrew it.
Say you put the bike in a repair stand, grab the right pedal and gently simulate the motion of someone riding the bike (always keeping the pedal platform horizontal as if your foot were there).  The body of the pedal will turn CCW relative to the crank.
Intuitively you would think this might help unscrew the pedal!  But in reality the clamping torque of the threads will be far, far greater than any friction in the bearings could generate.  Even if the bearings were to seize, it would be very difficult to unscrew the pedal (unless it was never tight to begin with).
Now consider someone riding the bike, putting weight on the right pedal.  This applies a force perpendicular to the ground, no matter where the foot is in the pedal stroke.  Relative to the crank arm, this radial force rotates CCW, which - via the process of mechanical precession - creates a CW torque on the pedal spindle (thus tightening it).  The rotations on the left side are all reversed, so it must use the opposite threading to prevent the pedal from coming loose.
Also see "Precession" on Wikipedia, from where the below illustration was taken (CC-SA).

A: I think pedal shaft threads are right handed on the right side and left handed on the left side is so that the pedals, which are asymmetric, will fit only on the proper sides. The bearings of the pedals are so low in friction that during pedaling there is completely insufficient torque to overcome the static friction of the threads which hold the pedals to the crank arms.
However, if there were any significant friction the net action of forward pedaling would be to unscrew the pedals from the crank arms on both sides.
This can be seen as follows. Consider the right side seen from the right looking from the outside end of the right pedal toward the crank arm. Imagine a spot of paint placed on the end of the crank arm on the outside face and imagine the crank turning CW. The spot of paint will be seen to rotate CW as the crank rotates CW. But we know that a right handed nut must be turned CCW as seen from the head of a bolt to tighten the bolt because this would be CW as seen from the nut end for right handed threads.      
A: In my opinion the easiest way to see this is the following:
take two identical screws, plug them a little into the pedals and then start to cycle. If you look at the bike from behind both the screws will move to the same side, one tightening and the other loosing. 
If you want them both to tight, then they have to move to opposite directions, so their helicities must be opposite.
A: I once built a custom bicycle, and used a crank from another bike. I found that the crank's design differed on the donor bike, and thus, would only fit my custom bicycle when installed in the reverse direction. I saw no other problems with this solution, until one fine Spring morning, while riding my newly fabricated custom bicycle downhill at great speed, the right-hand pedal un-threaded and dropped onto the roadway. Unfortunately, my right foot followed; as did my right leg. In what seemed to be nearly a full minute of slow-motion events, my entire body followed for a meet-and-greet with the road surface on that fine Spring morning. I lay crumpled and severely injured, against a metal road sign for an unknown period of time, until a passing motorist stopped and called 911. I was transported to Emergency Central, where surgeons labored for hours to stop the bleeding and to remove my custom bicycle from its painful resting place in my rectum. Fearing the worst, a priest was summoned by the hospital staff, and my family was notified of my condition. Fortunately, I pulled through, and am able to operate my wheelchair without assistance, thanks to many months of rehabilitation and therapy.
So, to answer your question; it matters little, why the pedals possess a tendency to loosen when a left-hand thread is installed on the right side. However, for the love of God; it would be in one's best interest to remember to be absolutely certain to place the pedal with right-hand threads on the right-hand side of the bicycle.
